Is there any salvageable hardware in your current machine at all? Otherwise you're short for a computer build period, let alone a gaming build. You're looking at at least $80 for a decent motherboard, $100 for a decent processor, $30 for ram, $80 for a power supply assuming you don't have a usable one, $60 for a hard drive, $20 for an optical drive, $30-$90 for a case (and you really don't want to skimp there), and a gaming PC really needs at least a $130ish video card. Thats around $570ish before the $130 operating system for a theoretical computer based on average prices and assuming a $70 case. A decent midrange gaming computer is going to run you closer to $750 before OS.
You can always build one in stages though, get the core components now, wait a month or two and buy parts as funds come available. If you are willing to accept slightly older style components, you can sometimes find "bare bones" kits, such as this one http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=7640252&CatId=333
$300 there would get you a lower end case, decent motherboard with room to upograde ram, decent lower end processor, a power supply sufficeint for a gaming video card, and 8GB ram with 2 free slots to expand later. You would still need the video card, hard drive and optical drive at a minimum with that (call it $230 more), but you would save about $100ish. thats again assuming you can aquire the operating system somewhere else (student versions, find an OEM key on ebay in direct violation of microsoft EULA, etc)
The main advantage to picking individual components rather than bundling is you get more control over your end product. I'd go with a quad core CPU and a better case for a starter PC personally (probably a cooler master CM 690 II case) but you have to go with the budget too. If you go with the AMD bundles you can save some more money there, though at the lower cost end there the Intel I3 processors and motherboards are pretty comperable in cost and speed.
You'll need a minimum of a 550 watt Power supply to drive a gaming video card. Check your current PC, it may have one. also make sure it has video card 6 pin PCI express power leads and an 8 pin core voltage lead for the motherboard. Optical drives are cheap, the amount of trouble you will save by going with a new SATA drive over trying to use an old, likely IDE one is worth the $20. Hard drives last 3-5 years on average before failure, if your drive is particularily old, its probably not worth trying to build a new computer around. Your existing video card, depending on age and slot type, etc, might work as a temporary unit until more funds came available to at least get you up and running.
Toss around some budget numbers and look at the various barebones kits out there, and if you want I can put together a component list to fit the budget for you. Newegg, frys, other comptuer chains also may have deals worth checking out.