Remove all you additional serial ports!!!
A mouse will ONLY work on COM1 or COM2 under Windows, never COM3 or 4!
As it is a Socket 3 Board you are running a 486 processor. I'm assuming the board has headers for the ports and not an I/O card. What it sounds like, is the ribbon cables from the COM headers on the mobo to the 9 way D Type connectors are the WRONG TYPE! This often happens if a computer has been cobbled together from parts.
Some serial ports need the pins wired 1-1 and others use a different method. Remove the 9 D cable from the computer case, pull back the plastic cover and look at the wiring. The red stripe ALWAYS goes to pin1, regardless of the connection method.
If the wiring follows the pattern red wire to pin 1, next wire to pin 2, etc with all the wiring following in sequence from pins 1 to 9, then this is a TYPE A Serial header. If the wiring starting from the red wire goes 1,6,2,7,3,8,4,9,5 (i.e. not following in numerical sequence but in physical position of the pins, alternating between top and bottom rows of pins - a neater looking cable!) then this is a TYPE B serial header. If the BIOS insists all the ports are enabled and your diagnostics are reporting the ports are ok, then you have a TYPE A header cable when you need a TYPE B or vice versa. Twenty seconds with a soldering iron will cure the problem, or look through your scrap box and find an alternate type cable.