|You obviously have no idea what you're doing.|
To start with, you haven't told us the make/model of your board or which CPUs you're swapping around. That info is important if you expect to get the answers you need. Same goes for the video cards. Did you bother to go to the board manufacturer's website & check the CPU support list before you started ripping into things?
It sounds like one of the problems is you're not installing the heatsinks properly. Did you thoroughly remove all traces of the old thermal compound & apply a small dab of fresh paste when reinstalling the heatsink? You can't reuse old paste & when applying a fresh layer, it MUST be done correctly. Too much paste is as bad as no paste. And I can't point you to the correct application instructions without knowing the CPU.
The beeping can mean a number of things. It could be an overheat warning, or it could be the video card isn't seated fully in it's slot, or if you messed with the RAM, it may not be seated fully in it's slot.