Turn the computer on first a moment or so before the monitor. At one time the system sent a momentary signal at boot to the monitor and if the monitor came on first it could miss the signal. That was quite a long time ago, but worth a try.
I've had the problem for over a year or more. I turn on the monitor first(it works fine) then I turn on the computer and I can see the hard drive lights working but nothing appears on the screen except a message that says "This monitor is Working". So I hold in the computer power button for 6 seconds and the computer cuts off. Then I quickly restart the computer and it works the second time. The computer works fine after I start it the second time. What could be causing this? I'm not going to take it to a repair shop and pay $95.00 an hour to figure out what's wrong. This is an older computer but it works fine. I've upgraded the memory to 316 mb, the hard drive to 30 GB (Maxtor), the video card and the OS to Windows XP.