I have taken the cover off the tower and examined the power unit. I do not see switch like the one you describe above. I see a switch that says " Compatibable Switch: with two arrows going in opposite directions of each other above the switch itself. It is in the down position. No one could have opened my case and changed anything.
Not all Power Supply Units have an on/off (I/O) switch located on the back.
I checked the power supply cord. it is good. I plugged it into a computer monitor here at work and it came on
Then I would assume another hardware component is the culprit.
I suggest you:
1. Remove and/or disconnect any hardware that is currently installed.
-- Be extremely careful when removing hardware or when working in the system case.. Unplug the power cable ledaing to the Power Supply Unit and be certain to take precautionary measures against electro-static discharge.
2. Continue to test the computer by adding one hardware component at the time. Once added, turn on the computer to see if it responds.
3. Repeat for all hardware removed and/or disconnected.
To learn more about ESD, see
this article.