These adapters use to be very common but now most PSUs have PCIe connectors. Still there is absolutely nothing wrong with using the adapter. I used to use them when I had a different power supply.
Honestly I am a little shocked this thread made it so far without more people pointing this out. This is the right answer to your problem.
While it is ture that both your power supplies are low quality, the 600w should be more than enough for your computer. A geforce 250 is not a very power hungry card.
Edited by Kirby1 - 1/27/11 at 9:08am