How to get my parents to let me go to a sick party?

As much as it sucks, there's no way to make them let you go to the party. It's probably for the best. Even if you say you won't drink, bad things can still happen. A friend of someone I know did that, and someone slipped something in her drink; and she got raped and she ended up in the hospital for it. It's best you don't go to a party like that.

I know the party has most likely been and gone by this time, but I have some ideas for future reference.
Tell your parents that you think they have raised you to be responsible and mature enough to go out with your friends and not get into any trouble. It's a bit of a mean trick, but either they let you go, or they are forced into admitting they didn't raise you well enough. When you're asking them, make sure you demonstrate this maturity, and talk to them in a level tone, and don't throw a tantrum if they say no or get angry. Let them know you're upset that you will be missing out, and ask them to reconsider.
It's also important that you take into consideration what was said in the answer above mine. You said you're not going to drink, but if you go to parties like this, make sure you keep yourself and your friends safe. It's great that you told your parents that there will be alcohol, because if you get in any sort of trouble, they should be the first people you call for help (or if it's serious trouble, emergency numbers).