This definitely sounds like the display cable is being pinched by the case. I would recommend keeping the laptop closed until you are ready to fix the issue, as if the cable keeps getting pinched it can rip or tear. This is fixable, you just have to use the iFixit guides to get to the Display cable, and then adjust it so that it is no longer being pinched.
It sounds like an issue with the connection between the power supply and the logic board, or the power button and the logic board. Also, what happens with pin 11 when you press the power button? If second LED is not visible when power button is pressed: • Verify power button connection to logic board • Verify power button functionality • Verify cable connection between power supply and logic board • Verify power supply • Verify logic board
Have you checked your keyboard settings to see if there is a replacement set for those keys? It seems strange that both 5 and 6 will change to 56. Some people will add replacements like this as a prank, so check in the "Text" tab of the "Keyboard" section of system preferences. Also, have you tried the keyboard on another device, and if so, did the problem persist?
Try taking off the bottom screws again, but leaving on the bottom, and try turning it on like that, just to make sure the screws were not causing the issue. If the device will not turn on at all, as in no fans, no sounds, nothing on the screen, its reasonable to assume something was damaged when you took off the bottom. If the device does turn on to some level, but wont reach the login screen, that is a different story. Could you clarify what happens when you try to turn on the device?
Did someone recently service the device, or is this a refurbished device? It sounds like either the display cables are getting pinched, or there is a loose connection. If you are comfortable doing so, I would suggest popping off the front cover of the lcd, and checking all the wiring, seeing if the problem remains if you loosen up the wires.
I had a similar problem, and my phone eventually bricked itself after I tried restoring a few times. I ended up sending the phone in to be repaired as I was still under warranty. For my phone, the problem was in the logic board, and the solution was a replacement of the bad board. I suspect this would be the only solution for you situation as well.