I had exactly the same problem, I literally tried all the buttons combinations, turned out it's a hardware problem, reconnecting battery solved it.
1) Remove back cover. It will definitely crack, sorry, so you need to replace it. You can get a 4 euro replacement from aliexpress.com, this is the link to the one I personally bought https://goo.gl/ko5b1e (it's as good as the original, Amazon is a rip off). This order also contains the mini screw drivers you need in case you don't have any.
2) BEFORE you unscrew the 5 screws, make sure you remember the place of each one, as putting them back in wrong places may cause the problem to persist. Should have the two smaller diameter but longer length silver screws on either side of battery. https://www.youtube.com/watch?v=jbvYl2Jw... (step at 0:40 until 1:07 in this video/ DO NOT CARRY ON WITH THE INSTRUCTIONS, no need to disassemble whole phone)
3) Jump immediately to step 9 (2:37 until 2:40, in the video, DO NOT REMOVE BATTERY FROM PLACE, just tick up the connector, then push it back down in again, make sure it's firmly placed.
4) Put screws back EXACTLY in the same place.