My Mac 3,1 isn't recognizing one CPU - Dual Xeon
This is almost certainly a hardware problem. As you're not sure that your second CPU was recognized after you unplugged and replugged it, it is likely that this is the event that caused the problem.
I would suggest shutting down the Mac, unplug power - and then remove the second CPU. Boot the system up and check that it works, and that System Information says 1 processor.
Then shut the Mac down again, unplug power - and carefully replug the second CPU. Boot up again and check System Information for the Processor Count.
If it still says 1 CPU, your problem is most likely either a defective CPU or a defective socket. The easiest way to check if to try with a different CPU. Perhaps you can get one cheap off eBay or perhaps you have access to one.
If it is a defective socket, then your options are very limited. With reasonable cost the only you can really do is to exchange the whole board.