PC won’t power up unless unplug USB devices

I’m having trouble starting up my PC. Unless I remove various USB devices from the back, and sometimes also remove the power supply from the back and then replug the PC will not start up.
(Nothing happens – won’t post at all).

Sometimes it takes me 4 or 5 goes of removing and replugging things until it starts up.

It also seems to be time dependent – if i try and switch on straight after powering down there does not seem to be a problem. However if left turned off overnight then it’s guaranteed not to start.

Grateful for any suggestions.