A $500 pc today is very doable and can be very powerful, if you're willing to build it yourself. If your old machine is more than a few years old, I wouldn't bother to try and save anything other than maybe the keyboard, mouse and whatever monitor you have. I'd do something like this...
$100 AMD quad core CPU- Athlon II or Phenom
$80 Motherboard to match above- Asus, Gigabyte come to mind
$50 4 gigs of Ram- get the fastest that matches the board above (I'd stay away from OCZ memory- I've had recent bad experiences)
$25 OEM decent CD/DVD burner
$50 Video card. I'd go for something with a gig of memory onboard and VGA, DVI and HDMI outputs (video on the motherboard uses system resources, and hey you might want dual monitors someday). You don't need gamer quality, but you want something decent. If you want to skip the video card, I'd go for more ram and maybe consider a nicer mobo.
$100 OEM system builders copy of Windows 7 64bit Home Premium. If you need the added functions of Pro, add $40. Thats mostly networking / remote access type stuff the best I can tell though.
$70 1TB internal hard drive (you can go smaller- my studio PC has a 320gig drive and I've been using it for several years). Western Digital or Seagate are really the only two brands I would even consider. SATA 3.0. Lots of people like to have separate drives for their OS and data. You can pick up another small drive for your OS for another ~$40.
$40 decent Case with a power supply. If you can find a case laying around, just spend that on a better power supply.
Thats about $515. right there. There's places to save- a smaller hard drive could easily knock off $15.
Now, that doesn't include a backup drive for your data. If your music is even kinda important, you will NEED to back it up. You can either get another internal drive and use a backup utility you back everything up which you can schedule to do automatically, or you could do a raid array or you could get an external usb or esata drive to backup to, but that means you have to remember to plug something in and make it happen. Obviously each of those methods has its pluses and minus.
Before you jump in to Windows 7, you'll want to make sure if you have any hardware you want to keep will work- sound cards, audio interfaces and printers would be the things to consider. Some older equipment doesnt have drivers for the new 64bit OS's.
I've been building PC's with parts from newegg.com for the past 10 years now. $500 has always been kind of my target mark for any current PC.
Hope that helps.