Thick layer of dust between cpu and fan pc wont boot could my cpu burnt out

Yes your CPU could be burned out, but I dont think it wouldn't give a signal, it would give a black signal.

As far as reusing parts go, what are the specs of the PC?

E4216, Intel D945GCCRG1 MB, Intel® Pentium® D Processor 925 @ 3.0 GHz

1. Blow dust out of POWER supply. Use a can of compressed air. Do not open PSU, they are actually very dangerous. Your system could be cutting out from overheating and under-performing power supply. might be good to blow rest of dust our of your case.
2. pentium D had thermal protection. It should shutdown before burning. However you are at the end of a long lifespan for a CPU (5+ years).
3.removing FAN is ok, however if the heatsink cam off teh CPU you will need to clean off the old thermal pad/paste and apply new past. Google 'artic silver' and goto their website and read their FAQs.
4.you can also visually inspect the capacitors on the MB to see if any of them are shot. http://en.wikipedia.org/wiki/Capacitor_plague

-- On rebuilding.

Look at a few used systems on EBAY, etc., before you decide to rebuild. I just spent $350 on a new laptop and got a system stronger than what you have. You can pick up a used Core 2 quad based system for less than that that will be much stronger than the pentium D as well as saving you money on the electric bill.