Help with ~$800 computer

Hey everyone. I should begin with saying that I am a total noob when it comes to computers. I have done my research and have a basic understanding of computer components, but I'm too big of a wimp to try and compile a list of parts on my own. I don't know what's considered good, and what's compatible. I was hoping somebody could give me a hand with that, and help me make this fit my budget.

Budget: Around $800
Purchase Time: Around this April
Main Uses: Gaming, Music Recording, Internet
What I Have: Mouse, Keyboard, Moniter
Overclocking: I don't think so.

It may be worth mentioning that I do have an old computer (long since obsolete, I think), so I could post a link to the specs and if it's worth just upgrading it or getting some parts out of it, please let me know as I'd be willing to do that.

Dell Dimension 4400:

For gaming, I don't need the highest level graphics if it's unrealistic. I'd be fine with mid-level on new games. The farthest out I can predict for games is Borderlands 2. I'd definately want this computer to handle that at around mid-level at a minimum. I'd like to use some emulators too, but that shouldn't be an issue if it can handle what I just listed.

I'd like for it to not need a cable to connect to the internet. I hope this is possible, as it's sort of a priority... I do have a router, and actually having a place for it to connect to isn't an issue.

I don't know squat about OSes, but I was thinking 64 bit Windows 7 as that's what people seem to reccomend. If I'm wrong, please let me know. I think that'll be around $100.

If student discounts are available on anything, I'm applicable for those.

I've never built a computer before, but I do have a friend who has that will help me. No worries there.

If any more info is needed, I'd be happy to give it. I really appreciate any and all help, and I'm sorry if I came off as unwilling to try, but I don't even know where to start.