This isn't really a question, more of an observation, but I don't think I've ever had a genuine "religious experience" where I have some kind of direct experience or connection with Hashem or the divine. I've been religiously observant (Orthodox) my entire life, and I have a yearning for some kind of profound mystical experience or connection with G-d (not sure how else to describe it). I sometimes find myself envying the generation that had the privilege to experience Matan Torah or other open miracles firsthand. All of the conventional avenues (mitzvos, Torah, davening, etc.) are great but they've never given me the profound spiritual revelation I wish I could experience. I wish I could experience Olam HaBa or Hashem speaking with me (even though I know it would probably be so overwhelming that my brain couldn't handle it). Does anyone else here feel that way?
Here are a few thoughts:
Learning Torah deeply, teaches one to switch from seeing nature as natural, to seeing it as miraculous, e.g. the story of R' Chanina Ben Dosa and the vinegar. Once one sees it as miraculous, you've achieved your goal. For example, if you see the feeling of love as just a physical manifestation of hormones affecting a nervous system, it will never be a spiritual experience, but once you start to learn how love has no place in a physical world, and comes from much higher, then every time you feel love, you have a mystical spiritual experience, and not even the lofty things, like love, but even the basic physical world of nature will do this. Here is an interesting article on this idea.
We are all numb nowadays, for various reasons including yeridat hadorot and others*. Part of the reason we might feel that life is devoid of spirituality is because of how numb we are. If we can only recall from our childhoods the true experience of intellectual excitement, the true feeling of deep emotion - and all the other amazing qualities of being a human being with a neshama in their proper expression - I doubt many of us would be struggling with this common question. See this answer for discussing walls around the heart.
As you've brought in your question, engaging in Torah, mitzvot and davening isn't working for you, as it isn't for many people. I would venture that for a lot of people, this is because they don't see Hashem as real, and this is one of Tanya's approaches in answering this common question. He is somehow abstract, distant and disconnected and therefore doing mitzvot becomes an abstract disconnected venture. Once He becomes real, and one realises that they are His mitzvot, and He needs us to do them, and the Torah is Him telling us about Himself. I.e. once He becomes an actual real someone to us, and we come to appreciate how we are His and He is ours, then every letter of Torah, and every detail of halacha becomes a true service of Him, and a profound spiritual experience.
All of the above I think would be useful for a lot of people, and certainly within reach of everyone. Higher things like ruach hakodesh and prophecy, the more commonly understood notions of "spiritual experiences" are likely out of reach for us until Moshiach comes... However, I think by yearning to connect to Hashem, you are doing alright, and I am highly optimistic that with this amount of yearning, and heartfelt davening, Hashem will bless you with success in this!
Until then, we should also be aware of a fair point, which is that we are here for one reason only: to do a mission. Having a spiritual experience isn't necessarily part of that mission for each person, in the sense that we aren't doing it for the reward, and the principle reward is not in this world, as we say every shabbat:
וְדַע, מַתַּן שְׂכָרָם שֶׁל צַדִּיקִים לֶעָתִיד לָבֹא:
I hope that helps.
* See also Ma'amar Hageula 1:4, even fruit is lacking in taste; Sota 48a; and further explanation Da'at Tevunot 40 p. 30
According to Pinchas Ben Yair, in the Talmud (Avodah Zarah 20B and other places), if one wants spiritual revelations they must work on themselves until, after a many step process, they are refined enough for G-dly revelation:
מכאן א"ר פנחס בן יאיר תורה מביאה לידי זהירות זהירות מביאה לידי זריזות זריזות מביאה לידי נקיות נקיות מביאה לידי פרישות פרישות מביאה לידי טהרה טהרה מביאה לידי חסידות חסידות מביאה לידי ענוה ענוה מביאה לידי יראת חטא יראת חטא מביאה לידי קדושה קדושה מביאה לידי רוח הקודש רוח הקודש מביאה לידי תחיית המתים וחסידות גדולה מכולן שנאמר (תהלים פט, כ) אז דברת בחזון לחסידיך
From here Rabbi Pineḥas ben Ya’ir would say: Torah study leads to care in the performance of mitzvot. Care in the performance of mitzvot leads to diligence in their observance. Diligence leads to cleanliness of the soul. Cleanliness of the soul leads to abstention from all evil. Abstention from evil leads to purity and the elimination of all base desires. Purity leads to piety. Piety leads to humility. Humility leads to fear of sin. Fear of sin leads to holiness. Holiness leads to the Divine Spirit. The Divine Spirit leads to the resurrection of the dead. And piety is greater than all of them, as it is stated: “Then You did speak in a vision to Your pious ones” (Psalms 89:20).
As stated in the comment above, Rabbi Tzvi Freeman writes:
In our own lives, He remains silent only when we do not know how to listen. If you are waiting for a booming voice from the sky to answer your prayers, you may be like the child who is riding her bike into a wall and waiting for her father to catch and stop her. But if you will look into your own mind and heart which G‑d has given you and the signposts He places all around you, there, if you seek with sincerity, you will surely hear His voice loud and clear—and find the brakes right on time.
In truth, in His absence He and His kindness towards us is found even more than in His presence. That is His greatness and that is His awesomeness.
As Rabbi Kaii mentions, learning Torah is one way. The Lubavitcher Rebbe would often emphasise that learning Torah will connect you with G-d, since Torah is G-ds inner will. However, in your question, you write that this is not working enough for you.
Please be reminded that in the end, Holiness is a gift, as the Mesilas Yesharim writes:
For that which is in man's ability to do is the initial exertion, pursuing true knowledge and continual thought on the sanctification of deed.
If you try and don't succeed, please bear in mind that:
The Holy One, blessed be He, will guide him on this path he desires to follow and imbue His holiness upon him, and sanctify him. Then this matter will succeed and he will be able to achieve this clinging with the blessed G-d constantly.
A great tip of the hat, can be found in the same chapter of Mesilas Yesharim:
One whose mind and intellect is always fixed on G-d's greatness, blessed be He, and His exalted holiness, such that it is as if he is actually among the lofty angels while still in this world.
You write that you wish that Hashem talks to you. To be honest, He does. Refer to my comment regarding Shmuel HaNavi and Eli. Shmuel did think that Eli was calling him, but in truth, it was G-d who was calling Shmuel. He did not know that yet. So too with us. We need to train ourselves, make ourselves "pure" in order to hear G-ds call. But, "a man is unable to do this on his own". You'll need to pray to G-d that He gives you "a listening ear".
The Mesilas Yesharim assures that if a person purifies himself, and follow the steps that he writes in that chapter, he will be able to cling to G-d.
The other answers are great. Just a small contribution:
There is a perception amongst some that having a cataclysmic religious experience will make things religiously better. Or, at least, that having this kind of experience every once in a while will only serve to better ones connection to Hashem.
I think the beauty of our connection with Hashem, and one which is endowed with the framework of Torah and mitzvot, is in 'bringing it down' to the day-to-day. The Torah tells us (Devarim 30):
12: לֹ֥א בַשָּׁמַ֖יִם הִ֑וא לֵאמֹ֗ר מִ֣י יַֽעֲלֶה־לָּ֤נוּ הַשָּׁמַ֨יְמָה֙ וְיִקָּחֶ֣הָ לָּ֔נוּ וְיַשְׁמִעֵ֥נוּ אֹתָ֖הּ וְנַֽעֲשֶֽׂנָּה:
It is not in heaven, that you should say, "Who will go up to heaven for us and fetch it for us, to tell [it] to us, so that we can fulfill it?"
יג: וְלֹֽא־מֵעֵ֥בֶר לַיָּ֖ם הִ֑וא לֵאמֹ֗ר מִ֣י יַֽעֲבָר־לָ֜נוּ אֶל־עֵ֤בֶר הַיָּם֙ וְיִקָּחֶ֣הָ לָּ֔נוּ וְיַשְׁמִעֵ֥נוּ אֹתָ֖הּ וְנַֽעֲשֶֽׂנָּה:
13: Nor is it beyond the sea, that you should say, "Who will cross to the other side of the sea for us and fetch it for us, to tell [it] to us, so that we can fulfill it?"
ידכִּֽי־קָר֥וֹב אֵלֶ֛יךָ הַדָּבָ֖ר מְאֹ֑ד בְּפִ֥יךָ וּבִלְבָֽבְךָ֖ לַֽעֲשׂתֽוֹ:14
14: Rather, [this] thing is very close to you; it is in your mouth and in your heart, so that you can fulfill it.
I think that the Torah is imploring us to imbue our life with purpose in how you deal with everything in the world. Connecting to Hashem is not 'beyond the sea' in a miraculous event, it is in the here and now in every little action that we do.
The path to Hashem is not in the unbridled miraculous mystical experience. It is in the day-to-day, our interactions with friends and family. Elevating the mundane experience. Imbuing every moment with awe and wonder.
Furthermore, I have had some experience with people who went through kiruv who were often looking for these kinds of "miraculous" moments e.g., the type from chassidic tales or kiruv books. But life is not really like that. If a person really feels that a momentous event was the sum total of what gives their life purpose, the strength of this anchor is only as deep as that event; which, believe me, wanes with time. Granted, the experience of Sinai was categorically different. But, for the average person, its important to build depth and breadth in all walks of life in all ways that you can.
Cast your net wide and your roots deep. Find meaning in the small and the big. Build relationships: a family, friends, community. The sum total of all of this is synergistic. The Jewish life lesson, as we can see from challenges of our forefathers, is that the Torah is not inherited (Avot 2:12). You need to earn your keep, shoulder responsibility and love Hashem. He gave us the Torah and mitzvot as a gift. We must cherish it, implement it, love Him, always search for Him and He will search for you.
With all the noise and hustle and bustle of the world around you, you should know that there is always a "still small voice" (Melachim 1, 12:19) to listen out for.