When plugged into the ps/2 port, you will need to have it plugged in before you boot up the computer, so that your bios can detect the mouse detected, otherwise the ps/2 port won't work. Once windows is loaded you shouldn't see a "new hard detected" window, it should just work as a standard mouse. Do other ps/2 mice work on that computer?
If other usb and ps/2 devices work, then its unlikely that the problem is with your computer, theres probably something wrong with the trackball or cable. Double check the cables and wires on the trackball and make sure everything is connected properly.