Modern CPUs will stop themselves from frying (talking about breaking stuff, I smoked a $600+ CPU back in the day; we all do dumb stuff). Try running it with the case open & a desk fan or something blowing into the case if you're worried.
Just using BIOS to check you can see HDD's or if you can send a picture over your video card isn't taxing the CPU.
Edit: You're correct, if BIOS dosn't see a CPU fan it's a bad sign. There's a chance you messed up your motherboard by squishing the metal stubs on the back against the case and/or frying something. But the fact you can enter BIOS is a good sign and, although entirely feasible, I've never seen a motherboard which can enter BIOS and is is also broken.