I have a DELL Optiplex Gx1 and my problem is when i press power button of my pc to start power comes but display not comes and then i press restart button and after pressing restart button display appeares and PC is working fine but next time i have to perform same thing for getting my PC booting

Found this guide:

DELL Optiplex Gx1

There is a diagnostic there as well as info on replacing the power & reset buttons.

Do you get any beeps after start before reset?

Something, perhaps the graphics, integrated ATI Rage Pro (AGP 2X) graphics, is not responding to the power on but is responding to the reset.

The above is the original onboard graphics device unless you have added an additional graphics card.

Hope this helps.

My son gets this problem and it as jephree says, a problem with the graphic card.