Help, do i need a new PSU?

Right so I have a new PC, it has a crusty Hyena 350W PSU.

I got an HD4670 because the PSU was so poor.

I am having some issues with my graphics card:

I've only been playing Q3 and WoW.

Q3 every so often - it resets the card but can continue playing after a 30 second freeze.
Wow when I Tab Alt sometimes - it seems to kill the whole card and i cant use any video applications until i reboot.

happens about once every 1-4 hours.

Bios is updated
I have the newest drivers available for the card.
I've tried various other tweaks from forum suggestions like turning off AA etc.

Does anyone think that this PSU will be causing the issue?

Now I can go upgrade to a Heyna 500W PSU with dual ball bearing fans for free, but will this solve the issue do you think?

The Heyna 500W PSU is around $50 NZ, the next cheapest thing I can find in what people would deem as a 'reliable brand' is a Thermaltake Litepower 430 Watt PSU for $90 or a Vantec ION2 460W PSU or a Enermax Tomahawk 400W for $100