i am having the same problem as you but i’m not using my power supply to power a computer, just a 12v fan and as a good DC voltage to test various things needing power. don’t like looking for batteries lol. a power supply (depending on it’s age) can be fooled into thinking that there is a motherboard connected to it and that the board is turned on. if you look at the 20 pin atx power connector on the PSU you will notice a GREEN cable. there will only be ONE and usually next to it will be a black (ground) cables. if you get a bent paperclip and short these 2 out (stick the paperclip in the green and any of the 2 black next to it making a connection) then stick the kettle power cord into the PSU and turn the PSU on if it has a switch the PSU will power up. you can then turn it off, connect a small 12v fan to the 4 pin molex (used to power the HDD or CD drives) by (if using a case fan) the black to the black next to the yellow, and the red on the fan to the yellow on the molex. that will give you a 12 v supply to the fan. plug it all back in and te fan will spin as the psu powers up. (nonsense info: the red, and black next to it, on the molex will give u 5v. and fan black to molex red, fan red to molex yellow 7v. that will make the fan spin slower and quieter. 5 slow and quiet, 7 faster and still pretty quiet, 12 fast and loud) BUT ANYWAY wait and see if the psu powers down then then. hopefully it will shed some light on the matter? hope it helps. my psu keeps on powering down. think it’s fauly. feels quite warm when it dows turn off but not too bad- my mobile charger is issentially the same thing and can get red hot sometimes!!

best of luck finding the problem. i’m sure its a faulty psu personally. new ones that run a higher wattage (yours might me insufficient if u have recently upgraded or ur psu has degraded with age) are really cheap if u look around. my little bro found a 600w good one for 17 quid new on the net.