I'd say, build a new one. The performance vs price margin between upgrading and building from scratch isn't that much. Especially if you only replace the motherboard, CPU, PSU and RAM.
Here's the minimum specs low down:
Dual core CPU: $50
Decent GPU: $50
2GB DC DDR3: $30 (4GB will cost double)
Decent 400W PSU: $40 (considering your current one is aging)
That's a total of approx. : $270. Pretty cheap IMO