To give you a definitive answer, we'll need the rest of your system specs:
# of HDD's
# of optical drives
Motherboard would be nice
Amount of RAM (not really necessary)
# of additional cards
In general I would say that 350W is not enough for today's or even a two year old system with that card. I would be shooting for 450W with at least 30A on the 12V line, if not a bit more. Again though that's a shot in the dark without knowing what your system spec's are, it could even be higher.