you should provide more context up front, if only a photo - without that, your description could mean all kinds of things.
But since you write it's a board, I assume its a normal ATX board, so well inside the Win 9x late 90s era.
Yes, serial mouse is an obvious choice. Also, many old PS2 devices like the Logitech wireless bases support passive adapter to serial/db9/rs232 port. They can be found easily, later ones were bright green.
Also, USB mice for DOS, well... I supposed that exists. Bit of a rabbit hole.
The engineer's solution, the PS2 mouse port is a "female" "6 pin mini-din" port, cheaply available retail and to be installed with basic soldering skills. Did not yet do that myself, but surely has been done before.
Somethin like this for a standard ATX board:
https://www.ebay.com/itm/332617314985
Of course, you first shold have a look, with a magnifying glass, whether some minor peace of metal has been bent out of shape or something and maybe apply some contact spray.