I have the super slim with a 500GB HDD and I had the issue where the light was red and when pressed, it turned green for under a second then went off completely, as if it had been unplugged.
The short term resolution was to plug it back in (so the light was red) and then unplug it for about half an hour (maybe less I didn't really test) and then when you plug it back in it should just switch on, but you would have to do this each time you'd like to use it
Long term would be to have the red light active and then leave unplugged for half an hour then plug back in and boot into safe mode and select 'restore file system'. It told me it had to format the PS3 but I saw now visible changes when it loaded back on (I think it formatted the 12GB of storage that my PS3 came with) and then it would switch on and off as it used to.