Tonight my sons pc just turned itself off while he was playing a game
He took the side panel off and there was a burning smell inside coming from the cpu cooler it was red hot,hes allowed it to cool down but when turning it back on there's no power no lights,fans dont spin up,tried a different power lead,different wall socket nothing
Is it likely to be the psu?
Spec-Amd 8350 processor,corsair 600wpsu,corsair cooler,gtx 970
Firstly, if you get to the stage where you can smell burning with anything electrical, the first thing you should do is isolate the item from the mains - switch off at the wall and unplug. And don't touch the pins on the plug. There's a slight chance you could get an unpleasant surprise.
If the cooler was, as you say, red hot, there's very little chance of the processor having survived. There's also a high probability of other components and cables having been damaged.
When was the interior of the case last cleaned? Sounds like a bad case of fluff build up on the cooler/components.
Allowing it to cool down and powering it up again was never going to help. Indeed, it may have made matters worse.
Unless you feel competent to test al the components yourself, and by coming here, I take it you don't, I'd be thinking it needs to go to somebody trustworthy to test/repair. Is the PC covered by any insurance?
That said, depending how old the PC is, you might end up better off/safer binning it and starting from scratch