Yeah that's a tough one. I come across this a lot with people who have either hand me down PC's or PC's that were just bought for them (not with gaming specifically in mind usually).
I usually recommend either saving up for a 350-400 dollar cheapy computer that you can at least have some more room in, or buy a new case, new psu, and then a new video card. But you're only as fast as your slowest part, so if your CPU is going to be a limiting factor as Jerreece stated, then I wouldn't even bother buying new parts.
Sorry bud! You can try this from ibuypower for $500 bucks:
AMD Athlon II DDR2 Configurator
Case ( NZXT Gamma Mid Tower Gaming Case - Black )
iBUYPOWER Labs - Noise Reduction ( None )
iBUYPOWER Labs - Internal Expansion ( None )
Case Lighting ( None )
Processor ( AMD Athlon™ II X2 250 Dual-Core CPU )
Processor Cooling ( Certified CPU Fan and Heatsink )
Memory ( 2 GB [1 GB X2] DDR2-800 PC6400 Memory Module - Corsair-Value or Major Brand )
Video Card ( ATI Radeon HD 5670 - 512MB - Single Card )
Video Card Brand ( Major Brand Powered by ATI or NVIDIA )
Motherboard ( ASUS M4A785-M -- AMD 785G Hybrid CrossFire Chipset w/8-ch HD Audio, Gb LAN, S-ATA Raid, USB 2.0, 1 PCI-E MB )
Motherboard Add-on ( None )
Power Supply ( 600 Watt -- Power Supply - SLI Ready )
Primary Hard Drive ( 500 GB HARD DRIVE -- 16M Cache, 7200 RPM, 3.0Gb/s - Single Drive )
Data Hard Drive ( None )
Optical Drive ( 24X Dual Format/Double Layer DVD±R/±RW + CD-R/RW Drive - Black )
2nd Optical Drive ( None )
Flash Media Reader/Writer ( None )
Meter Display ( None )
Sound Card ( 3D Premium Surround Sound Onboard )
Network Card ( Onboard LAN Network (Gb or 10/100) )
Netbook / Notebook Bundle ( None )
Operating System ( None- Pre-formatted Hard Drive Only )
Monitor ( None )
That should definitely be enough to get you going