I removed the CPU heatsink/fan unit from my desktop computer and put it back.

Now when I turn on the computer, it starts to boot, gets to where it starts checking devices, then just turns off completely. I've restarted it 5 times but it keeps turning off, will never start booting windows at all.

I even completely removed the heatsink/fan thinking it might not be fastened correctly, but even without it, the computer still begins to boot then just turns off all of a sudden.

One thing I also did was remove a thick layer of (what I thought was) dust from the top of the CPU and the bottom of the heatsink. Reading the answers below, it seems that I removed the hardened thermal paste.

What can I do to get my computer to boot correctly again?

EDIT: I just turned it on again (without the heatsink/fan unit attached), it got to where it found its memory, then it said, "CPU fan error!" and turned itself off.

So I need to put the CPU heatsink/fan back I figure. But the problem is I can't get the four little pegs to fasten securely into the mother board, the little plastic tips bend this way and that and I can't get all four of them to get into their holes all at once, I've gotten three in but not all four. Is there a trick to this that I don't know?

EDIT: one of those little plastic pegs broke of, so I'm just going to get a new heatsink, thanks AlbertoPL for the tip of getting one of these so I don't have to deal with those little clips anymore.

Solution:

I bought a new LC-Power fan for 15 euros ($20) which came with a little bag of thermal paste, was a bit difficult to get even the new pins in the mother board, you have to press so hard you think you are going to crack it, but finally worked, computer started immediately first time and fan is MUCH quieter!