|"the fan in the back of the CPU powers on, as does the fan on the processor"|
The CPU IS the processor. I believe what you're referring to as the "CPU" is the tower/case? The "fan in the back" is either is a case cooling fan or the power supply (PSU) cooling fan.
Why would you switch the HDD because of a power issue? If you haven't already done so, switch it back. And I doubt resetting the BIOS is gonna do anything unless you attempted to overclock & went overboard with the settings?
The 3 most likely candidates are the PSU, CPU or motherboard. You may ask why would the PSU be a possibility if the fans work? There are several different voltage rails (+3.3v, +5v & +12v)...it could be that just one of them fried leaving enough power for fans & lights, but not enough to boot an entire system. Unfortunately, power issues aren't easily diagnosed thru a forum. Make sure all you connections are tight & that there's no dust buildup within the case. You didn't try to remove the heatsink/fan (HSF) from the CPU, did you?
The bottomline is you have some troubleshooting ahead of you.
"If my answers frighten you then you should cease asking scary questions" - Jules Winnfield (Samuel L. Jackson) in Pulp Fiction