There will be a front panel header for the power button going to your motherboard named as Power SW. This is the cable from your cabinet power switch. When switch is pressed, it closes the circuit between the two pins that its connected to on the motherboard which powers on the PC. if this cable is shorted for some reason or the switch is getting struck and closing the circuit on its own, then the power can turn on..
So, remove it and try powering on/off your UPS a few times. If computer doesn't turn on this time, but does when the cable is connected, then its possible that the switch or cable is at fault.
Good Morning... will do same soon and reply here .... Thanks for help/suggestion