|You turned on the PC and heard fans spinning and maybe drives too. You saw LEDs flashing on the front panel so you assumed the PC was OK and the problem was with video.|
Maybe it is but probably not. For most systems one beep is normal. No beeps is not good. The activity you're witnessing is what happens when 5 and 12 volts are applied to the hardware. It doesn't mean the motherboard or even the power supply is good.
Some systems are built with cheap components--both motherboard and power supply--and tend to fail because of that. For example, on a motherboard the capacitors near the cpu often get 'puffy'. After awhile they don't work right and you're left wondering what is wrong with your computer.
Besides low quality components check my # 2 here for some other things to consider:
Ding dong the witch is dead. . . .