If you get no video, and no beep codes when you first boot the computer, I would suspect the CPU, MB, or Power supply.
It also could be that the CMOS reset jumper is in the clear position.
Double check all jumpers and dip switches on the MB.
A weak CMOS back up battery could also create strange problems.
How do you know that the power supply is good?
There are at least 4 different sections of the power supply. Just because the fan runs, or your drives spin up does not prove that their is no power supply problem.
Double check that the power supply connectors are seated fully into the MB.
Remove and re-seat the RAM modules. Check for corrosion on the pins. Very important if the MB uses SIMMs.
Verify that the CPU socket latch is closed tight.
Next, remove all plug in cards except the video card, and disconnect the drives from the MB.
If you now get the boot screen, add the other devices back in one at a time until you find the culprit.
Otherwise, it's time to start swapping out the main components.
If you swap in known good RAM, CPU, and power supply, then it must be the MB.