|I'm probably stating the obvious but if you never ever see anything on the screen then it has to be a hardware fault of some sort.|
3 beeps usually mean a RAM fault (although the computer make and model number would help). If you are prepared to look inside you could remove the RAM then clean its edge connectors with a pencil eraser. Also pop it in and out a few times to clear any oxide off the sockets themselves.
There are memory tests that you can download if the above doesn't help.
Always pop back and let us know the outcome - thanks