The laws of Shabbat apply only to Jews, so someone who isn't Jewish is doing no wrong whatsoever when they watch TV on Friday night.
For Jews, as pointed out in the comments, there is a difference between turning on a television and watching it. Turning on the TV directly activates a flow of electricity which is forbidden by G-d as communicated to Moses in the Torah. While there is no question that switching an electrical current on or off on Shabbat is a transgression of Torah law, what exactly is wrong with it is the subject of discussion. See this question for more detail.
Watching TV on Shabbat, taken in isolation, is a transgression of the commandment to make Shabbat special, different and distinct from the week days. The source of this commandment is from the prophets whose communication from G-d came after and is subservient to what Moses taught. It is consequently a less severe transgression than actually turning the TV on, in the sense that the punishment is less (the Torah prohibition is punishable by death in the most extreme case, but not the Prophetic command), but is unequivocally equally binding and is taken equally seriously.
Similar considerations about using electricity and making Shabbat mundane apply to turning on and/or listening to a hi-fi on Friday night. Basically, any forms of entertainment that use electricity or otherwise break Shabbat laws are also forbidden. Singing without a microphone, though, is practiced in synagogues and at Shabbat meals around the world as a beautiful expression of the holiness of the day. It can be profoundly moving and a highlight of the Shabbat experience. I recommend it.
Whether one will "go to hell" for turning on or watching TV depends on the person doing it. The judgement of G-d takes into account every aspect of the person and his circumstances. As it says in Deuteronomy 32:4
הַצּוּר תָּמִים פָּעֳלוֹ
כִּי כָל-דְּרָכָיו מִשְׁפָּט
The Rock, His work is perfect;
for all His ways are justice
Specific mention is made of a person's upbringing by the Rambam, who declares that a Jew who has not been raised to keep the commandments can not be considered a willful sinner. Such a person is classified as a tinok shenishba, a "captured child", as if they had been kidnapped from their Jewish family and raised by non-Jews. Wikipedia has a reasonable summary.
Thus, to the degree (measurable only by G-d, and possibly the person himself) that he chose (consciously / unconsciously, knowingly / in ignorance, deliberately / accidentally, under influence / on his own initiative) to transgress the command of G-d he will be punished. Nothing is ignored.
This punishment is not imposed immediately, or else we'd all be struck by lightning as soon as a stray thought entered our heads. In fact, it is considered an expression of mercy on G-d's part that He delays punishment to give us an opportunity to repent. Repentance (teshuvah in Hebrew) is an essential, central and everyday concept in Jewish life. The Talmud states that the nature of man is such that without teshuvah he simply could not endure. The fact that we will sin is accepted, so it then falls upon us constantly to return to righteous behaviour.
How does one do teshuvah according to the Jewish tradition? The Rambam writes that three components are required: Regret that one did the sin, Commitment for the future not to repeat the sin, and Confession to G-d. Probably the hardest one is committing never to do that sin again, but it seems to me that can be a process rather than a binary decision. See the excellent answers to this question.
To apply these principles to your question: To repent for watching TV on Shabbat a person must accept and agree in their heart that they did wrong by turning on and/or watching TV. This means they wish they had not done it and if they could they would 'undo' the past. They must sincerely resolve never to do it again (which should include taking practical steps to avoid transgressing by accident or being overwhelmed by temptation). Finally they must confess aloud to G-d what they did, apologise, promise not to do it again, and ask for His help to keep His commandments in future.
Repentance actually does have the effect of 'changing the past'. Someone who has done full teshuvah for some sin is considered as if he simply never did it, and it will not be held against him in his judgement. Further, the most profound application of repentance can actually result in a net gain in spirituality, not just a return to 'zero balance'. This is the concept of teshuvah me'ahavah - repentance motivated by intense love of G-d, rather than fear of Him. On the other hand, regret for past actions can also erase good deeds...
Simply, if you do teshuvah you will not "go to hell".
What if someone doesn't do teshuvah, or does only a partial teshuvah? Then their recompense will find them according to the decision of G-d. The punishment may be applied during their lifetime or afterwards. It is considered far better for a person to be punished while alive ("in this world") than after death ("in the next world"). This is because the nature of those two states affects the nature of the punishment. This world is ephemeral and of small worth compared to the Next, so punishment here is temporary and less encompassing. The spiritual world (also known as the World of Truth) is 'beyond Time' and is far more significant, for want of a better word, than this one, so punishment there is qualitatively worse. I am being vague, but these ideas are lofty and I understand them only a little.
Punishment achieves atonement. Suffering is corrective and redemptive, rather than punitive. If I remember my Maharal correctly, the disorder that a sinner brought to the world must naturally be visited on him if he does not do teshuvah, but once it has been imposed he is cleansed.
About the nature of "hell": In Judaism one's spiritual existence after death is not divided into separate "places", like Heaven, Hell or Purgatory. The limit of my understanding is that after death a soul is faced with the life it led in totality. Like I said, the Next World is 'beyond time'. In this 'World of Truth' the true nature of a person's actions and his relationship with G-d is inescapable. There is no forgetting, ignoring or evasion. Your life is there before you, and your reward and/or punishment is to inescapably experience it on a spiritual level with all barriers to understanding and appreciation of your actions removed. To the extent this accords with the Truth it is blissful beyond description. And vice versa.
The idea that you get 'points' for a mitzvah or lose them for an aveirah (sin) is disconcertingly unsophisticated. Firstly, no actions are overlooked. No deed can 'cancel out' another deed. What's more, an act can be at once both good and bad. All these calculations are taken into account by the immense depth of G-d's judgement.
[Wipes froth from his mouth] Ahem.
So, the answer to your question is... "It depends". It's relative. And it's not inescapable.
If this question is actually applicable to you, and you are feeling guilty because you watched TV... relax. The G-d of the Jews is not out to get us. :-)
He is a caring, loving and understanding Father who literally has our best interests at heart in the deepest way. He knows you beyond even what you know yourself and understands where you're at, where you're coming from and where you long to be. Rather than concentrate initially on the extensive body of instructions that apply to the Chosen People, strive to develop a personal relationship with Him in your own way. Talk to Him. Pour out your heart to Him. And listen for His answers in the things He brings your way.