Unplug the power. Take out the card in question. Reseat all the other cards you left hanging. Nail down the loose power connectors with ty-wraps. Apply power. Does it work?
If not, unplug every plug in board you think you can spare. Unplug
*BOTH* the power supply connection and ribbon cable (or SATA connector) to every drive in the system. Note I said BOTH. Also, unplug the keybaord, mouse, iPod, printers, and everything else you've go hung on the machine. You're now down to basics, with just the power supply, motherboard, and possibly a video card. Turn it on and see what happens. If that works, one of the devices you removed or unplugged is fried.
Exactly? No. You would need some kind of PCI bus tester. Something like this:
I have a really simple one that just shows the power bus voltage, and does a POST display on 2 LED's. Paid about $35. If you're planning on doing this professionally, you gotta get some test equipment.