Hi!
You should check the contact pad underneath the PS/ Home button for any gunk that might have gotten in there over the years. Also, make sure the rubber pad that actually makes contact with the contact pad is alright and not torn/ broken. If everything is fine, replace the ribbon cable between the screen part and the bottom part of the console.
PS: Follow [guide|1189|this guide] until step 19/ 20 to get to the contact pad.