mobo is defective.
sounds like the mobo not working correctly. possibly because of bad RAM, or likely PS/2 connector is broken or picofuse is blown, etc. try to verify this with a volt-ohm meter, it should be +5V on pin 4 (and pin 3 is ground)
2 □ 1
4 3
6 5
if the mobo is really damaged, you should either replace it or get it repaired (must not be cheaper than get a 2nd-hand one from ebay). Or you may try to attach a USB keyboard to bypass POST if the mobo and BIOS support.
good luck.