Just to clarify what the issue is. UPS (Uninterruptible power supply) Is actually a battery.. That keeps your system running in the event of a power failure.
I think your meaning. PSU (power supply unit) Powers your desktop system, connected to the mobo, vid card etc etc.
Your system automatically turns on and you have to use the switch at the back of the psu to keep your system off?
Id say the button on your case used to turn the power on/off is malfunctioning (known to happen overtime by usage) getting stuck and always thinking it's on. Let us know if my clarification is right and we can help further!