Yes I agree, if your Keyboard is disabled then you can't interact with the system... However you are still able to disable it and even boot windows up without a keyboard present. You just can't type anything, you will have to use the mouse all the time instead
Yes you are correct.... The BOIS is set, by default, not to boot up the system if a mouse or keyboard or Floppy Disk drive doesn't work or missing.... But you CAN change this, I don't know why you want to boot the system up without a keyboard, but there you go lol
slap me for stating the obvious but have you tried changing the batteries in your keyboard, dont know if it makes the pc drop the keyboard if there is no signal from the keyboard due to no power.
also, check if ALL the lights are on (num lock / cap lock / scroll lock ) on the reciever.
i have had this a few times where everything has frozen and mouse/ keyboard have not worked (tell tale sign was all three lights lit even though scroll lock was off). way around this is to power down the pc, unplug the keyboard and mouse PS2 connectors and then plugging back in. power up and all was well. dont know what caused it but after a re-install it seems to have stopped happening.
good luck anyway (my keyboard/mouse is a Genius model KB-16M wireless set)