Power On Switch:Use a jumper wire from the Green wire to ANY Black wire, in the back of the 20-pin ATX main power cable's connector.
http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20The Green wire is the Soft Power On wire. Abbreviated as PS_ON)ANY Black wire, you see going into the back of the main power cable, is a Ground wire.The main power cable is plugged in, as shown in the photo to the far right. The Back of the connector is where the wires go in.The preferred jumper wire is a straightened out paperclip, and bent into a U-shape.The middle of the U is wrapped a few times with black plastic electrical tape.This taped area is for your fingers and thumb to hold onto.Turn the U upside down, and the 'legs' are what is used.One leg slides down into the Green wire's socket hole, RIGHT NEXT TO the Green wire.Has to go pretty far down in the socket hole, as it has to touch a metal terminal, at the end of the wire,
http://www.molex.com/molex/products/datasheet.jsp?part=active/0002081202_CRIMP_TERMINALS.xml&channel=Products&Lang=en-US[The back of the terminal where the jumper wire touches, is to the left. The tangs on the left, haven't been crimped over the insulation of a wire yet.The right side, is the round tip that is seen in the middle photo, of the connector in the Playtool link ]
The other 'leg' goes down into ANY socket hole, with a Black wire in it. Slides past the insulation of the wire, and touches the metal terminal at the end of the wire.Power Supply is plugged in, jumper wire is used.The contact made is no more than 2 seconds. The Power On switch is a Momentary Contact Switch.Power Supply comes on you have a bad Power On switch.You can also test a Power On switch with a multimeter. Just be aware as said, it is a Momentary Contact Switch, and you will get brief readings on the multimeter, every time you push the switch.(IF, the switch is good)
http://www.directron.com/atxswitch.htmlMotherboard:Check the Electrolytic Capacitors. (Radial Aluminum Electrolytic Capacitors)
http://www.capacitorlab.com/visible-failures/index.htmVisually check for signs of failure.For additional questions please post in a Comment.Regards,joecoolvette