Well.. trackball trouble?
A good question ..so, you know the answer already

DOS:
- You have a DOS driver for the TB/mouse in your autoexec.bat, YES?! Works in DOS ..for a while..
? What version of DOS are you actually using?
? What are the machine specs? Memory? .. Memory all counted & conventional memory available for programs..? (type MEM at the DOS prompt..)
? Have you tried other (DOS) mouse drivers?
? IRQ conflicts? -> Printer port (usually irq 7) comes to mind; that was the root of all evil in the "Dos time". Shouldn't really affect mouses in any way (anyway)...
Tiny XP:
- Yeah, I've heard of that way to waste your time

- Still, have you at least double checked your PS2 connectors..?
- Again, running out of memory?
Well, trackballs/mouse controllers, who knows:
http://forum.arcadecontrols.com/index.php?topic=66155.0Actually, I think that if you can't get it working with two or three different open source/whatever drivers it must be the motherboard - or the PS2 connector - that is faulty.
No real help here I'm afraid.
psycho.