Thank you so much!! After hours searching the net for lights not turning on or not charging, I gave up thinking the controller broke. Luckly I gave one last try and searched for getting hot, which it was a bit, and found this!
I had disassembled the dualshock 4 to fix the triangle button which was getting stuck. After that the controller simply wouldn't work. With your help I just cleaned the flat cables a bit and it came right back to life :D