Apparently if you ever hook up a USB keyboard to a Windows 7 or 8 computer it will turn off PS/2 keyboard support. Why it does this is anybody’s guess, but I assume it’s some opinionated MS tech forcing people to ditch their old clackity IBM Type-M keyboards once and for all.
To get it working you simply have to open regedit. Then find the following key:
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\i8042prt
Edit the Start value and set it to 1. For me it was set to 3, and setting it to 1 and rebooting left the keyboard functional instead of turning it off after Windows started.
[EDIT May 20th]: I have also found that if your machine goes to sleep and turns off the USB ports it will disable the keyboard. Make sure you use a USB port that stays active while the machine is asleep. For best results, always do a clean boot before trying to use a PS/2 keyboard with a modern system. PS/2 keyboards are required to be present at boot for them to work.