Well then, you'd better take all the covers off, the doorbell and the disboard, and see if you can see where the cables run, shouldnt be too hard, if the 'bell has its own 'breaker, follow the live from the breaker and you'll find the cable that runs out to the push and the 'bell, I spose there could just be a single live going to the push and another single neutral going to the 'bell.
If you pull the main fuse or trip the main breaker then you can use a long wire on a meter with a buzzer to buzz out either ends of the wires.
I know you arent me, however if I was to look at the issue as a job I'd be inclined to chop out the cables for the doorbell and the computer room and fit anew, as I wouldnt want to risk an installation with question marks over it.
Are you in the us with 110, or in the uk or somewhere with 240?
You could threaten the'leccy with reporting them to the electrical governing bodies, but if they've allready botched it then you'll probably only get more of the same.