I find the liturgical and rabbinic descriptions of the atonement process on Yom Kippur challenging. Without a Sanhedrin to mete out punishments for intentional sins, and no altar to bring offerings to atone for unintentional or un-witnessed sins, the chance of ever starting the year with a clean slate seems bleak. But we are also led to believe that sincere repentence wipes out all sins. Can we ever start with a truly clean slate? Or will we still be held liable for sins we don't get punished for in this world?
Repentance absolves all sins. However, depending on the nature of the sin, full atonement may be immediate or may be contingent on something else.
- Violation of a positive commandment (that does not carry karet) is forgiven immediately upon repentance. (1:9)
Violation of a negative commandment (that does not carry karet) is partially forgiven upon repentance, but only fully forgiven on Yom HaKippurim. (1:10)
Violation of capital offenses or offenses that carry the penalty of karet, are partially forgiven through repentance and Yom HaKippurim, and are fully forgiven through suffering. (1:11)
Violations that cause desecration of God's name are only fully forgiven upon death. (1:12). These are sins which are done to anger God (Hilkhot Yesodei HaTorah 5:13).
Interpersonal sins require restitution to the damaged party as well as his forgiveness. (Hilkhot Teshuvah 2:11)
So as far as positive and negative commandments, one will indeed start the year with a clean slate (provide that he repents). Even the more severe sins carrying the death penalty or karet do not require the Sanhedrin or the sacrificial service to achieve atonement.
In summary, no, not ALL sins.
There are several aspects to answering your question, and I couldn't get to all of them, here.
But to start, Talmud Yevamot (don't know exact page) explains that Yom Kippur never atones for sins between one person and another until that person requests forgiveness, personally. The method becomes a bit more complex if the wronged person is unreachable or dead.
Another more difficult example is atonement for lashon hara and rechilut (gossip, slander). How would you now how many people got the bard word about someone, and how could you really recover the damage already done?
Yet another concept is inferred from your mentioning that we don't have a Bet Hamikdash and we carry the sins of our ancestors. This concept is hinted to in a few places in our daily prayers (esp. Tachanun) and the fact that we still don't have a Bet Hamikdash is an indication that we have not yet been forgiven.
Finally, what about all those sins that we did during the year, but on Yom Kippur, we forgot about them and didn't mention them in our confession? We're still responsible.
The first perek of Shevuos, summarized in Rambam's first perek of Hilchos Teshuvah, says that certain sins are atoned for immediately by teshuvah, certain ones are atoned for by Yom Kippur, though Teshuvah delays the punishment in Olam HaBa, and certain sins are atoned for with suffering, though Teshuvah and Yom Kippur delay the ultimate punishment. Chillul Hashem is the harshest of all; its atonement comes only with death, and the above three delay the punishment until then.
Also, as discussed in the last Mishnah in Yoma, there's another requirement for sins between man and his friend, which is asking for forgiveness.
As the Rambam (ibid.) notes, none of these sources say anything about karbanos. To the contrary, our Teshuvah takes the place of the karbanos, and, as the Midrash (Vayikra Rabbah 7:2) points out, is even better than karbanos:
One who does Teshuvah is as if he went to Yerushalayim, built the Beis HaMikdash, built the Mizbeiach, and offered upon it all the karbanos in the Torah, as the passuk says, "The offerings of Hashem are a broken heart."
Emphasis mine: not just the applicable karbanos to the sin in question, but every last one of them.
Yes, Yom kippur atones for all sins according to torah, for one year.
"He shall then slaughter the goat for the sin offering for the people and take its blood behind the curtain and do with it as he did with the bull's blood: He shall sprinkle it on the atonement cover and in front of it. In this way he will make atonement for the Most Holy Place because of the uncleanness and rebellion of the Israelites, whatever their sins have been. He is to do the same for the Tent of Meeting, which is among them in the midst of their uncleanness. No one is to be in the Tent of Meeting from the time Aaron goes in to make atonement in the Most Holy Place until he comes out, having made atonement for himself, his household and the whole community of Israel. Then he shall come out to the altar that is before the LORD and make atonement for it. He shall take some of the bull's blood and some of the goat's blood and put it on all the horns of the altar. He shall sprinkle some of the blood on it with his finger seven times to cleanse it and to consecrate it from the uncleanness of the Israelites. When Aaron has finished making atonement for the Most Holy Place, the Tent of Meeting and the altar, he shall bring forward the live goat. He is to lay both hands on the head of the live goat and confess over it ALL THE WICKEDNESS AND REBELLION of the Israelites - ALL THEIR SINS - and put them on the goat's head. He shall send the goat away into the desert in the care of a man appointed for the task. The goat will carry on itself ALL THEIR SINS to a solitary place; and the man shall release it in the desert." Leviticus 16:15-22
Dr. Michael Brown comments on this: Notice carefully what the text says: The High Priest is to confess over the head of this goat "all the wickedness and rebellion of the Israelites - all their sins" - and "all" means "all." Notice also that the text specifically speaks of the "wickedness" (or "iniquity"; Hebrew, awon) and "rebellion" (Hebrew, pesha‘, meaning willful transgression) of the Israelites, not merely their unintentional sins.
However the sacrifice of the Messiah should be superior to the animal sacrifices.
Rabbinic scholar Solomon Schechter summarizes the Talmudic teaching that suffering and death atone for sin, with specific reference to the death of the righteous:
The atonement of suffering and death is not limited to the suffering person. The atoning effect extends to all the generation. This is especially the case with sufferers as cannot either by reason of their righteous life or by their youth possibly have merited the afflictions which have come upon them. The death of the righteous atones just as well as certain sacrifices [with reference to b. Mo’ed Qatan 28a]. “They are caught (suffer) for the sins of the generation. If there are no righteous, the children of the schools (that is, the innocent young children) are caught for the sins of the generation” [b. Shabbat 32b]. There are also applied to Moses the scriptural words, “And he bore the sins of many” (Isa. 53:12), because of his offering himself as an atonement for Israel’s sin with the golden calf, being ready to sacrifices his very soul for Israel when he said, “And if not, blot me, I pray thee, out of thy book (that is, from the Book of the Living), which thou hast written” (Exod. 32:32 [b. Sotah 14a; b. Berakhoth 32a). This readiness to sacrifice himself for Israel is characteristic of all the great men of Israel, the patriarchs and the Prophets acting in the same way, whilst also some Rabbis would on certain occasions, exclaim, “Behold, I am the atonement of Israel” [Mekhilta 2a; m. Negaim 2:1]. 269 – Brown, Answering Jewish Objections to Jesus, Volume 2, Theological Objections, p. 158
Your concern is genuine regarding sacrifices today without the temple and becomes an issue to ponder and investigate in light of this traditional evidence that the sacrifices have been unacceptable- even before Temple destruction.
"R. Nahman b. Isaac said it was the tongue of scarlet’, as it has been taught: ‘Originally they used to fasten the thread of scarlet on the door of the [Temple] court on the outside.28 If it turned white the people used to rejoice,29 and if it did not turn white they were sad. They therefore made a rule that it should be fastened to the door of the court on the inside. People, however, still peeped in and saw, and if it turned white they rejoiced and if it did not turn white they were sad. They therefore made a rule that half of it should be fastened to the rock and half between the horns of the goat that was sent [to the wilderness]’. . . . If you assume It was R. Johanan b. Zaccai [who made the rule], was there in the days of R. Johanan b. Zaccai a thread of scarlet [which turned white]? Has it not been taught: ‘R. Johanan b. Zaccai lived altogether a hundred and twenty years. For forty years he was in business, forty years he studied, and forty years he taught’, and it has further been taught: ‘For forty years before the destruction of the Temple the thread of scarlet never turned white but it remained red’. Further, the statement of the Mishnah is, ‘After the destruction of the Temple R. Johanan b. Zaccai made a rule’. [What says] the other [to this]? — During those forty years that he studied his status was that of a disciple sitting before his teacher, and he would offer a suggestion and make good his reasons." Footnotes: (28) After the High Priest had performed the service on the Day of Atonement. V. Yoma, 67a. (29) This being a sign that their sins had been forgiven. Rosh HaShanah 31b, Babylonian Talmud, Soncino Press Edition