Is this a new machine?
For normal computing needs 300 watt is fine.
A graphics card 'pulling' 350 watt will only do so in a high activity mode such as Games a graphics editing
If you are into that then potentially the PSU will not cut it and shut down I would imagine.
Going back to the original precept - if it's new send it back,or if it is a replacement GC then the PSU should be upped to say 400/450 watt