look at the PSU label on the side, find the column labeled "+12v" and tell us the number of amps it says there. if its less than 17, i wouldnt even think about it. if its 18-20, u might be ok.
since its an FSP 350w, i think it will be around 15amps or less, so u will need a 400W PSU or more. cooler master, corasir, antec are all good brands.
jsut because it says 350w, doenst mean it will actually do 350w safely for long periods of itme. there is probably fine print that says u shouldnt exceep 250w and that 350w is the peak output.