I have a 5 year old pc and unfortunately I can't afford the complete new system that I really want just yet. It's frustrating not being able to play recent games because it's really struggling with graphics power (It has an nVidia 6800). The solution is obviously a new GPU, but I'm in two minds about what spec I should go for. I have a LGA775 board with a Pentium 4 3.4GHz that hopefully won't bottleneck from the single PCI-e, so I could theoretically run anything up to a GTX 480 or HD 5970. This would mean a new PSU as the current 350W has no chance, but this adds an extra $100-150 to the upgrade. I've been looking at a HD 5770 as a good mid-range card that will fulfill my needs, but this too would require a new PSU.
So to the question....
Are there any GPUs that will run on a 350W PSU and still give me the performance to run modern games well?

Thanks in advance