Remove the Power cord from the PSU to discharge the Capacitors in the Power Supply. Then press the Power button for 10 seconds to discharge the Capacitors on the Motherboard.
Plug the power cord back in and see if it will start. If it does replace the Power Supply Unit (PSU).
Reseat the Central Processing Unit
Faulty Fans, Dust and Grime build up on the Heatsink restricting air flow. Remove the Power cable from the rear of the System and disconnect the Video cable. I would give the inside of the case a blowout with compressed air. When blowing air through the fans make sure that you physically stop them from spinning, as they may generate power and damage something. Use an Anti-Static Wrist Strap to ground yourself or by placing the back of your hand on the Power Supply Unit and not moving your feet. This will prevent electrostatic charge from building up and by not taking this precaution it is possible that you could inadvertantly cause damage to the PC from an electrostatic discharge.
Then remove the Heatsink, giving it a thorough clean and reseat the CPU applying new CPU grease. If the Fans spin freely when you give them a spin they are probably OK. If there is resistance replace them.
Clean the golden edge of each memory stick with a soft rubber/eraser, remembering not to touch the golden edge of the memory stick. Check with one stick at a time, remembering to disconnect the power from the PC.
Also check the Capacitors around the CPU for swelling or bulging.
