Windows should pick it up automatically. If you haven't used the serial port for anything else before I'd follow darry's advice and check that your serial port is working properly, preferably with a small loopback adapter that you can easily build inside a spare DE-9 plug. If the port is good the most common failure mode for an ordinary wired mouse is the cord fraying near the mouse end due to the constant flexing of the cable. Using a multimeter in continuity mode you can find out if any of the wires had broke inside the cable - if that's the case you can cut the cable and reconnect the remaining good piece to the mouse PCB.
The serial port works, i tested it with PUTTY and HyperTerminal to my main machine and Duke Nukem 3D over 9600 baud. I have heard that the common DB9 serial ports supply +5 volts, however the mouse says +12, -12 14mA on it... Not sure what this means though
The end connector seems loose, like the cable itself feels very floppy. It's a direct serial plug, no adapter. I wonder if the wire itself may be busted. If that's the case, is it possible to just replace the cable itself? I know it kind of ruins its "originality" if i do that, but honestly so does it being totally busted