Note that if you place a disk drive next to any CC computer, and put a disk with a "startup" file on it in the drive, then the computer will boot from that file on its next startup. Say they put an empty startup file on the disk, that means it simply boots to the command line prompt, giving them full access to do whatever they want with the system.
The only way to prevent someone from rebooting your computer (Ctrl+R) is to block their character's physical access to it.
Hence I'd recommend rigging something up involving wireless modems. The terminals the players CAN access sends off what they type to a hidden computer that 1) has the password list and 2) has the ability to open the door.
You can alternatively do what you were originally thinking - rig up a monitor for them to interact with - though since they can't "type" into a monitor this means that you'll have to manually code "buttons" for players to push on that monitor yourself, which is more work. It also means you need a hole in your wall for the cable, which players could potentially navigate a turtle through. Come to think of it, it'd be pretty easy to have a turtle dig along cables until it finds a computer, then take its place and start pulsing redstone signals at random - would be a good "skellington key" or sorts for such doors.
