When the on button is pushed there is an audible click and the LED's light for second, then nothing. The fan is not running, drives not spinning, just nothing. This does not happen everytime. Usually if the machine has been moved or bumped in any way, then push the on button, it will power up just fine. Have checked the power cords, power supply and source and found no problem. There are no peripherals attached. I am thinking it is the power switch and/or possibly the solenoid but looking for other possible solutions.

With the symptoms you describe, my guess is power switch. Other possible causes would be
CPU
Motherboard
Ram
Badly seated card
But if you bump it and it works, that would rule out all of those except cards not seated. Check the power switch. Reseat all cards and memory. Try another power cable.

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