I'm only making an experienced guess here;
The converter wouldn't help, if you're wishing you would have found it.
If you only have one rail, and it only supports 20a, I tend to agree with BFG tech that your new card isn't getting enough juice.
If it isn't getting enough power, it is more likely to have memory or transfer bus corruption, and, oddly enough, overheat.
I have an Aerocool zerodba 500w power supply. I bought it for way too much money at a brick and mortar store. (I'd just gotten a new card that required more power, and I didn't want to wait on shipping).
It's lowest powered rail is rated 17a (it has two rails)
It has two PCIx connecters that go to one cable.
I use it to power two 7800GT cards along with a Opteron 185, 2gb of DDR400 memory, 4 ide drives, 1 sata, and several fans.
Though I'm probably near my max power limit, it serves me quite well as is.
I'm guessing that if you got a good 600+ power supply with 2 or more 12v rails that combined are more than 28a, and at least one PCIx included, you'd be ok and have a bit of room to grow/upgrade later.
Whatever you do, as you might have already learned through the interwebs, don't skimp on a cheap PS.