Bobcat,
When you try to start the computer do you get your normal quick single beep startup chime?
If you are not getting any beeps then you likely have a bad motherboard or CPU. Though I would suggest this.
1. Unplug every component (just check that your CPU's heatsink is secure, there is no reason to detach your CPU yet)
2. Then only plug in your power cables, internal speaker, front panel connectors (power,restart and led's) RAM and Video card (assuming that you have a dedicated video card).
3. Turn on the computer you should get to the BIOS if your CPU, Motherboard, Video Adapter and RAM are in good shape. If at this step you do not get any boot screens listen note what the computer does when you press the power button.
-Do you get a quick single beep? Then you board passed initial self tests for memory, CPU, and motherboard functionality. I would then presume that the video adapter has bit the dust.
-Do you get multiple quick beeps, extended beeps or a mix of the two then there is a problem with a core component. (check your boards manufacturer to find out the meaning of the specific BIOS error code)
-If you get no reaction when you press the power button then you could have a bad power supply, motherboard, CPU or Power Button (you can test this by swapping the power button and reset button where they attach to the motherboard then press your reset button). Since you said that you get lights and a quick spin of the fans with your new power supply I would suspect that your power supply is fine.
4. If you are able to get to your BIOS then turn off the computer and plug everything back in something probably got knocked loose.