Hoboape said:
I was wondering if anyone has had a problem like this before and do I need a new PSU?
Those components all sound perfectly normal and should work fine together, assuming it isn't broken a 600W Corsair branded power supply should easily have enough juice to run that system.
<spoiler= Wall of text under here, all the things I can think of that may relate to your problem>
I) Number one thing is to check all the plugs and connections are properly connected and that the inside of the case is clean and not full of crap.
II) When you switch it on does the board make any loud bleeps? If yes that indicates a power, memory (RAM) or temperature error and the stoppage is to protect hardware, it usually means that the power supply is broken or the RAM isn't installed properly.
III) Can you define 'nothing' in a little more detail please.
IV) That the lights and fans are coming on mean that you have power, your graphics card should be getting power from the same unit as the rest of the computer (if the 600W Corsair unit is the only one in the case then it has to be powering the GPU) so if it is spinning up that would also indicate you are getting power. Although that does not guarantee the PSU is delivering the correct amounts of power.
V) If you have a manual for the motherboard please get it now, you will need it.
If you have no manual you can download one from Gigabyte's website here: http://www.gigabyte.eu/ but you need the exact model.
The exact model is useful to know anyway, Gigabyte makes thirteen models of GA-P67A and they have different features, it will be on the manual and printed on the board itself.
You motherboard may have a POST readout on it, this looks like a little tiny digital clock readout.
If when you switch it on this starts displaying a number or letters before or after the cut out, see what they mean in the manual. With any luck that will tell you the exact nature of the failure without any fiddling.
VI) If there is no POST reading, on the board, it may appear on screen before the cut off, again watch for it, write it down and check against the manual.
VII) Last thing, if you can get to the EFI/Bios menu (check in the manual how to do this). Go from there to the hardware monitor, in theory the computer is forced to stay running as long as it has power in these menus, so you should be able to see how much power your Power supply is delivering to where, what temperatures parts are runnning at and various fan speeds. If any are outside of the accepted minimum/maximum for the board they will probably be highlighted, if so write them down and report back here or to the board's manual again.
Hope some of that is useful