I am unable to use any keys on my keyboard to remap keybindings and in-game none of the default controls will work. I tried to use all 3 variants just to be sure, and tuend numlock on and off and tried those separately as well.

Possibly related, my computer will not allow me to install directplay, which crashes Army Men II when launching. Army Men I launches fine.
Edit: Launching using administrator solved the directplay install problem, but the controls still do not work. (the mouse does work, so I can aim in a circle [for what it is worth])

It won't let me edit my post again, but the keyboard DOES work in Army Men II.

Jup, sure does. The keyboard layout is a bit weird and don't forget to activate your Numpad, otherwise you're in trouble!