I can't help you with the serial number search. I think that is going to take a phone call and the help of an actual human and the physical machine. I don't recall ever seeing serial numbers in any spec I have looked at online.
However, the On/Off switch on a computer is a very simple and dumb part. Any switch will work electrically. In fact, you could cut off the switch with some snips, pull the 2 wires through the switch hole, and just touch them together to start the computer! (Not recommended though).
So any switch you can find that will fit in the case will work. If you are handy you could mix and match the parts to get it to work.