Usually, with a truly dead CPU, the system wouldn't boot at all. There's usually not much in between there. It either works or it doesn't.
The only exception is when you've been OC'ing to the limit and the CPU starts to degrade. When that happens, BSOD's will occur frequently until death a short time later.
With a broken pin, if it's one that really matters, it wouldn't boot at all (there are some that are redundant and/or not that important that won't cause problems).