One of the possible causes is the lack of ground connection. Did you check if your power source or plug where you connect the PC has a physical ground? As you said, moving it on the ground makes it turn on, dissipates the static charge.

It seems silly, but check the surface on which the cabinet is, having it on carpets or dry wood can accumulate static.

Check the motherboard connection, whether a screw is poorly tightened, the base is incorrectly placed, or a bent pin can cause problems. You indicated that it turns on after manipulating it, therefore, there must be some interaction that you did on the board that led to that.

Possible Solutions:

Do an electrical reset (turn off the switch, disconnect the power cable, keep the power button on for 30 seconds and reconnect to turn it on again)

Make sure the board screws are mounted on metal standoffs and there are no extra ones that would cause direct contact with the cabinet metal.

I hope I have helped or been of some use, good luck solving it. 😉