[M. Bison]

If the graphics card/mobo port was bad the motherboard usually does some beeps to say it can't detect it. In this case the fans usually still spin up. My money is on a bad motherboard/PSU.

That really depends on the damage to the graphics card. If you were to say, damage one of the gpu memory modules, then it'd probably still power on fine. However, you'd probably either see lots of incomprehensible symbols all over the screen, or a big black/gray plume of smoke coming from your computer case. At which point, it's probably safe to say you fried the mobo too.

The symptoms suggest a failed power supply -- it sounds like one of the rails has failed. If a replacement unit doesn't solve it, it could very well be the motherboard. CPUs very rarely fail, however that would be my third guess.

Any other failed components would still allow the CPU fan to spin, provided they are properly connected, which I would assume they were prior to opening the case.

Yeah, it's probably the power supply or mobo.