No 350W is not good enough for a 8800GTS G80. These cards are power hogs and I lost a PSU due to this card and it was a 450W 20A antec with a Pentium D 820 65nm 2GB DDR2. I would look for a better PSU cause if it goes you may end up buying more than just a PSU.
7970 3GB *Unlocked* = 8 Threads
5770 1GB OCed = 2 Threads