The ball-mouse may have a broken wire in the cord. That's
a reason for the mouse cursor to stop and start at inconvenient
times. You've already cleaned it, so I don't have to tell
you that step first. To repair it, you cut off the suspected
section with the break in it, and use the remaining wire to
restore things to the way they were.
Usually the break, is right where the wire passes through
the mouse housing. That's where all the stress is concentrated.
Here, someone pretends to burn the shit out of a component
on the mouse PCB. To give you some idea of the fun ahead.
This style mouse might be a bit harder to repair, because you're
dealing with a connector. First step, is to record wire
color, and which pin each color goes to. If you ruin the
connector while repairing it, you can always solder the
bare wires into the appropriate holes, after removing the
connector on the PCB.
http://thumbs.dreamstime.com/z/repair-computer-mouse-10703093.jpg
Note that, inside the mouse, there are a ton of springs and wheels
that can fall out. Using a digital camera, take a picture of the
mouse from several angles, while it is still "in one piece". So
you'll be prepared if the guts fall out. I've spilled one
of those damn things on my table, and it took a lot longer
than I want to admit, to put it all back.
*******
With respect to USB mice and the "turquoise adapter".
That adapter is purely passive. It just routes the USB
pins to a PS/2 connector pattern.
Your mouse could be a dual-protocol mouse or a single
protocol mouse. The turquoise adapter usually ships
with the dual-protocol mouse. You cannot put the
dual-protocol adapter on the single protocol mouse
and expect it to work. Nothing will happen. The rodent
will be unhappy. So don't do that.
At my house, the two turquoise adapters, belong to two
identical Logitech Click! Optical Mice. I do not
attempt to connect the adapter to my other mice,
because no good will come of it.
The mouse has the magic, not that adapter. The chip
inside the mouse, senses whether USB bias or PS/2
bias is connected, and applies the correct protocol
for the electrical conditions it finds. The adapter
contributes nothing to the exercise. The mouse is
the "brains" of the operation. If the mouse does
not have the right chip type inside it, that
passive turquoise adapter cannot change things.
You can test the USB ports on your Compaq, with
a USB flash key. If the key shows up, you know the
USB port has power, and the data pins work.
You could test the USB mouse, on some other known-good
computer.
The OS has HID drivers, for things like mouse and
keyboard, and I doubt that is missing. There could
be a problem with Plug and Play. There could be
an inappropriate UpperFilter driver in place.
But there's no reason to suspect anything of
the sort.
HTH,
Paul