I would recommend trying the serial mouse. They work just as well as PS/2 mice. Unless you have a dire need for all of your COM ports, try the serial mouse.

Also, try and figure out if the beeping is coming from the OS or the hardware itself. Look in your motherboard manual and see if you can find anything about the beeping. I've never seen windows beep like that before, so I suspect it is a hardware thing.

Try doing a defrag and scandisk of your hard drive, and if possible, do a cleanup (get rid of all the junk). And of course, it would always be a good idea to get a new computer If you want to custom-build it, I can help you choose the correct parts and stuff (but it is also fun to research it yourself)