Start with the bare minimum (no gpu, single stick of ram, no drives) and see if it'll POST then.
If it does, you can start adding components back in and see where it craps out.
If not, disconnect everything from the PSU and short the 'power supply on' pin to ground on the 24 pin connector (look up a picture for reference).
If the PSU turns on and it can power some fans, then it is probably good. If not, you need a new power supply.
You could verify this by borrowing a PSU from a different system (possibly from a friend) and see if your system turns on then.