Ok. This is what I would try to see if the power switch is bad. BE VERY CAREFUL AS YOU TRY THIS!!! Take off the side panel on the case. Look at the motherboard. Find the connector that connects to the power switch; it should be in the lower right corner of the motherboard. The connector should be labeled as "Power" or something like that. CAREFULLY remove the connector from the motherboard. It should pull right off. OK. Now the pins of the motherboard should be exposed. Plug the monitor, keyboard, and power connectors into the computer. Take an insulated screwdriver and carefully touch the metal of the screwdriver between the two metal pins on the motherboard where the power switch connector came from. The computer should power on!
If the computer powered on, the power switch is the culprit. If the computer still refuses to power on, the problem is much more serious, and is likely your motherboard....
Best of Luck