My 27" iMac won't startup unless I unplug it. before I start it!

I have  a 2014 intel i7 27” iMac that needs a repair and I think it is in the power supply. I start it and it boots up ok and then after a few minutes it goes off entirely without any notice at all , dark screen and nothing works. If you push the start button nothing happens, no starting sound at all. Then if you unplug the unit and plug it back in and push the start button it sounds and starts and boots up for a short time and goes out again. Thanks so much for your help. Tom