Hey ASF,
It looks like you have SOME power, being that the fans are working and you see lights. One obvious question, is it possible that the problem lies with the monitor but the computer is atually on?
Assuming that isn't the case, have you made any significant hardware or software changes recently? If not, there are a few possibilities.
The first thing I would do, is try to power up with another power cable; they are cheap and people usually have an extra one lying around. Also, check that the voltage switch is set correctly on your power supply. I would also try plugging it in to a different outlet, and use a different power bar, or if you are feeling risky, plug it directly into the wall to ensure your power bar is good. After that, check that all of the connections in the computer are sound. Check your RAM and video card that they are seated correctly. Check all of the case connections to the MOBO. If the connector from your "Power on" button to the MOBO is loose, it could be causing the problems. There is an outside shot that your CPU isn't seated correctly, but I REALLY doubt that.
After checking all connections and ensuring it is not a power from the wall issue, odds are it's a component failure in your system. More than likely, it is your power supply or your motherboard, with the power supply being the most likely culprit.
There is also a SLIM chance that it could be your RAM, Video card or processor, but they are unlikely.
Good luck! Computer problems suck lol.
Rylant