A1398 Common issues
The MacBook Pro may appear to turn off. The fans will still spin and caps lock will still work. The cause is that the GPU is losing power due to flexing and brittle solder around U8900 (GPU Buck converter). Solder U8900 with an iron and leaded solder. Triple check all joints under a scope.
L2013-2014 (820-3662, 820-3787)
Screen off computer on or crashing: Sounds like the FDMF6808 chips are failing and causing black screening. You can try fixing this by replacing all 3 of them with NEW FDMF6708 or FDMF3030 chips from a reputable source from Mouser or Digikey. I’ve had good success doing this. Possible software fix linked here
Very unlikely to be a screen or screen cable issue. If you’re not getting image when this happens, then it’s not related to backlight either. Very very small chance it’s a GPU/CPU issue unless the fall you mentioned was major. This model has an issue where from flexing those chips tend to fail and cause the device to not wake from sleep/randomly shut down due to CPU VCore dropping out. Machine will stay on but basically never wake from sleep at times similar to what’s wrong with yours. If you’ve never messed with microsoldering before, I would recommend sending this to someone who has experience fixing this issue. If you have done board repair, then this repair is a little tedious so you want to make sure you get GOOD chips as the ones claimed to be new in China often end up sanded down garbage to look new
If you have dedicated graphics on your board then the above fix have a 5% chance of succeeding, its not considered worth it to try and fix.
If you have internal graphics, aka no graphics chip on your board then you have a 95% success chance, so the above fix is likely to work.
2015 dedicated graphics (820-00162, 820-00426)
These boards absolutely require a good charged battery to fully boot into macOS. As usual it's not uncommon to get 2 or 3 bad batteries in a row so make sure you are using a known good one, one that for sure works with others 15" 2015 DG boards.
With a bad battery or no battery, the machine will reboot during or at the end of macOS boot. In this case disconnecting the touchpad often allows it to boot fully since it causes throttling and lowers the overall power consumption of the machine.