I'm out of clues. The hardware keys have worked for me several distros on those computers (but admittedly not on Mint).
The only idea I have right now it to boot to one or two Live CDs of something other than Mint and seeing whether you can use them to connect to the projector.
It might help if you post the information about the video card (running lspci
in a terminal should reveal that) and the make/model of the projector. That information might enable someone else to have a clue.