Sounds like a lot of fun things going on there Jeff. Your last sentence makes things interesting though, so lets toy with that for a minute!
Get hold of a linux live-cd and run your machine up under that for a while - see if the strange behaviour continues or if it stops completely. The Ubuntu live CD also has a set of system tests installed on it which can test your memory etc very thoroughly! This will help to tie-break between software and hardware. If the CD tray no longer opens by itself, then there may be a problem with the drivers for it. Given that you have replaced the mother board and CPU, the only thing left of the USB connectors is the wires in the chassis and the software. Wires don't normally go bad, and certainly not all of them at once, so I'd put my money on the software.
You might want to set up for a boot-time run of chkdsk and see if there's a hard drive problem that could be causing corruption of files?
As regards a linux install, yes, you can install both on the hard drive as dual boot. If your drive is formatted with FAT you could even put them in the same partition, otherwise you can use gpartedit to adjust the partitions and make room for linux