Broken Computers

OK, seems like my chain of counterfeit coin puzzles has come to an end. New puzzle time, I first learned this one on the forums at xkcd:

You have N computers, some of which are broken and some are not, and you do not know which ones are broken. You may have any computer run a diagnostic on any other computer to find out if it is working. If the computer running the diagnostic is working it will tell you correctly if the second computer is working. If the computer running the diagnostic is broken, it will give you a random answer.
It is guaranteed that over half the computers are working, find a strategy that is guaranteed to locate a working computer using no more than N-2 diagnostics.

By "it will give you a random answer", I mean that it will say 'this computer is working' or 'this computer is broken' each with 1/2 probability. It is worth nothing that strictly more than half the computers are working, so if there are 10 computers it is guaranteed that at least 6 are working.