What's the OS and shall I assume a PS/2 or USB port is otherwise not available?
Serial Mice with wheels were few and far inbetween if they did really exist at all; wheels were really after their time. If you don't have Microsoft's IntelliPoint driver installed, do so. It's likely a specific protocol as if I recall, there was no true standard protocol for that over serial.
My server is running Windows Server 2003 R2, my dad's desktop is running Windows 7 Pro, and my old windbag computer is running Windows 98SE.
I just installed the drivers, still nothing. Speaking of protocols, does protocol (Serial) mean setting the baud rate, stop bits, bits, Flow Control, and Parity to (example for a 2-button serial mouse: 1200bps, 7 bits, 1 stop bits, Xon/Xoff [Hardware, or none] - Flow control, and None [Even, Odd, Mark, Space] - Parity) to make the mouse work? My dad had set up a protocol when we used an IBM mouse on it; the mouse worked back then. Wouldn't hurt to test the port settings until the mouse works.