I have the very same trackball and it would not work on a couple of dell pc's which I have, It would work on an old machine with ps2 connection on the motherboard but not the dells addon port.
It also would not work with a ps2 to usb adaptor, I had to purchase an active ps2 to usb convertor for the dell to see it as mouse.
I assume that the trackball is generic ps2 protocol and not like some ps2 mice which are dual ps2/usb protocol which work with the simple adaptor.
Summing up, save yourself anymore hassle and buy an active ps2 to usb convertor and plug into a usb port, job done.
Rob
Edit: just read you hadn't it plugged in at bootup, try that first, might work but didn't for me. If it does happys days, if not active converter will sort you out