OK, I downloaded qbasic, added it to the boot floppy, booted the HP Pavilion and ran the mouse demo program. It reported that there was no mouse available for demonstration. I tried this on three machines, all with the same results. I think at least one of the mice on these three machines does in fact work (e.g. a non-PS/2 mouse which I can't use on the HP Pavilion), but the non-HP Pavilion machines aren't running any programs that use mice. So, I'm a little suspicious of the demo program.
At first I thought there was a typo in the program because there is a routine called mouseinit and also something called mouseint, but that is probably ok. Maybe, if there is an error in the program, it has to do with the stuff immediately following mousein: in the program, i.e. a block of what looks like assembly language that might be making some assumptions about the hardware or interrupt settings.
With Linux running on the HP Pavilion, I looked at /proc and did find a mention of /dev/psaux, which is the mouse. I ran kudzu and now have it run every time the machine boots. It consistently says that a PS/2 mouse seems to have been removed from the system. On the other hand, I think I saw a boot message detecting the mouse port. So, if all of these observations are correct, the OS can detect the mouse port but not the mouse.
I'm not good at cleaning anything, certainly not my apartment, and I don't have a successful track record of cleaning mice: I think I cleaned one other one in my life and couldn't get it to work and simply replaced it. So it is quite possible that whatever I did to clean the mouse was inadequate.
Let me ask you this: is there any direct way to test a mouse without using a computer? E.g. can I test it using a Radio Shack voltmeter, which also measures amperage and resistance? After all, the issue should really be whether certain connections on the mouse are any good. That sounds like a purely electrical problem, and for that reason I'm cross posting this to sci.electronics.misc.