Yes most fortunate, without going off topic too much using an underpowered PSU adds wear to not only the PSU but also other components MB, CPU, Ram, add on cards etc and eventually something will give, as rshaffer61
has already said the symptoms you describe are typical of a short but PSU issues can manifest themselves in many/various ways.
EDIT: The PSU output of 350W is better but still not brilliant, the brand and efficiency rating make all the difference ie an Antec PSU with 80% efficiency for example.
You may like to consider this until RonShaffer61
checks back in;
Best couple of suggestions I can make would be first remove the MB and do a bare bones set-up on a piece of cardboard (make sure it is larger than the MB) only connect the PSU, the GFX, keyboard and 1 stick of Ram.
You will then need to short out the 2 power on pins on the MB header to get the PSU to activate, you can use a small flat bladed screwdriver or a paper clip bent into a U shape, this is perfectly safe if you do not touch anything else, the idea is to see if we can get a BIOS screen if you do you can then add one component at a time until you find the problem component, you must power down and remove the power cord from the wall before adding a component, second suggestion try a known working PSU and third suggestion try and loan an ordinary PCI graphics card (not pci-e) again to try and get a BIOS screen.
Apart from an incorrectly placed stand off check for stray screws or bared wires.
Edited by phillpower2, 11 April 2011 - 01:21 PM.