Had the exact same problem as you after my MBP had fallen off the bed.
Had a completely black screen - not even a backlight. Tried tapping on the casing near the display cable and pushing the black bar in at the back of the laptop but it did nothing. Tried resetting NVRAM/PRAM - nothing.
I realised that I could log in and suddenly the keyboard and Apple logo lit up and the backlight was working so I figured there was something wrong with the screen. Connected it to an external display and got nothing but then I tried booting it whilst pressing cmd + D and it worked on the external display, however it completely shut off as soon as I tried to log in.
Eventually realised I was going to have to open the case to see if the display cable was damaged. I've never done this before so was a bit nervous but I ordered a screwdriver set from Amazon and waited a couple of days. Followed the guide posted above to open the case and located the display cable. Tried wiggling it a little and screwed the case back together and frustratingly it did nothing. Almost gave up at that point and was resigned to the fact that I'd have to take it to get repaired.
However, I gave it one last go except this time I disconnected the battery and the display cable and plugged them back in. Put it all back together, turned it on and BOOM! Screen turns on, everything back to normal! So relieved that I've fixed it!
Thanks for all the advice in this thread, you're all lifesavers!
Rob