Series s won't turn on after unplugging it.

I fully shut down the console through the power options menu, then once the light on the xbox logo is off I unplug it

Nope, I'm not using any betas

It first happened about 2 weeks ago. I wanted to move it, so I turned it of and when I tried to turn it back on after a few minutes it wouldn't work.

I tried again after a few hours and then it worked.

Well, the console eventually died completely, wouldn't work at all.

I changed the psu now it's working fine. Turns out that was the problem after all.

Very easy and cheap fix, if anyone else has the same problem just go for it and replace it

Are you not using an insider build / beta OS in your console?

Also, when this started to happen? Do you know?

Thanks, I can advise you two more things before considering a hardware issue:

A. Do a factory reset but keeping games and apps
Go to settings > system > console info > reset and then select keep my games and apps (or if you don't mind select remove everything)

Just to let you know, your saved progress and game licenses are attached to your Microsoft account and on the cloud

B. Perform an offline update for your console. In that way Xbox system will be installed from scratch.
For this you need a USB and PC to format it and transfer files provided in the link below (with detailed steps and requirements):

https://support.xbox.com/en-US/help/hardware-ne...