I'm not much older than you, but I'm a parent to a 4 year old daughter, who is pretty crafty at getting her own way.
Let me tell you, the moment anything happens to that computer of yours, your parents will instantly know it's your fault. You may think you're crafty now, but they've known you since you were a baby, they know how your mind works.
As mentioned above, the most likely outcome is that they will make you go without a computer and use school computers (possibly not even allow you to use your mums) until you've saved enough to buy yourself a new computer.
They probably won't let you touch your college money either. Your best best, is to discuss and agree with your parents that you will get a part-time job and use the money from that to save up for a new computer.
I'm pretty sure most parents will agree to that. You worked for that money, it's yours. There's plenty of small jobs around, and $50-100 saved per week will get you a refurb apple laptop in 10-15 weeks tops.
If you're in any way techie, you know an old computer, even one like yours is still pretty useful. Don't kill it - reuse it.
Suggestions:
1. As said above, get a backup external. NOW. They're dirt cheap. At the moment you are risking losing all your work and papers any second. Moving some files onto it will release some space. Get a 160gb or 250gb or even a 1TB backup. Or you could use the new drive as a primary internal, and use the 80GB drive as a secondary storage drive.
2. As said above, get new fans / clean the fans you have. This will help with the noise. If you buy new fans, get bigger ones maybe - they will spin more slowly.
3. Max out the RAM. 512MB is nothing. You can probably get 1 or 2 GB into it for a few dollars. It'll make a world of difference.
4. Reinstall XP. This is where the backup drive will help. Clearing out 8 years of cruft will give your computer new life. Once reinstalled, avoid adding new programs, and turn off as many graphics options as possible. Maybe stick to XP, Office, Firefox / Chrome, a video viewer, and allow nothing else to be installed.
5 (optional) Look at getting a new faster processor, but it's unlikely to be worth it.
6. (optional) look for a better graphics card on ebay or something, but it may be difficult to figure out which ones are compatible.
If you are low on money, I would get a smallish backup drive, upgrade the RAM, clean the fans, and reinstall XP.
That'll give your PC a good few more years while you look for a job and save up for a new one.