Okay, I did want to verify that your mouse was indeed serial compatible before suggesting more involved fixes.
Does the mouse from the other PC work on this one?
It is not impossible that the manufacture made a firmware change that causes the mouse to not work with a serial adapter anymore.
If the mice are of the same lot, and you have verified that the new mouse does function as a serial mouse, then we are left with registry/driver issues.
I would look in the registry for keys left over from your previous mouse driver. Getting rid of those may correct the problem.
You might also try an older version of the driver for the new mosue, as the older version may support your older hardware and W95 better.
I have corrected some W95 mouse issues by deleteing the mouse and port from device manager, booting up and shutting down with the mouse disconnected, and then connecting the new mouse, and booting up.
Chas