Most likely the graphics chip if it didn’t take a fall if it did fall most likely lcd broken you’ll be able to tell if its lcd when the computers off you can look for lines. google the command to boot it in diagnostic mode I believe its command D while the Mac boots up
Connect the OEM lcd check if it has apple logos and connect it to pc put in DFU mode and restore it. New software might help the issue sense its only working with aftermarket. If you have other OEM lcds try a different one maybe you broke the digitizer on the OEM screen.
Your battery unfortunately has probably gone bad google the model number and see if its repairable lucky in 2018 theres a video for everything. I don’t know if Ifixit will have parts for it try ebay if not look for good vendor.
So you know i just purchased a iPhone 8 brand new from apple updated the device to new iOS and my iPhone is already at 94% battery life. apple put this feature in because of there lawsuit a tried and true way to see if you have a bad battery is to check a few things. 1. is the battery swollen, lithium ion batteries do have life spans and will go bad just like your AA batteries swelling is a sign the battery is starting to go. 2. does the phone slow down and get laggy around 20% battery life, thats the phone attempting to slow down to keep the phone battery lasting longer its a sign battery could be replaced 3. the most annoying one do you charge your phone to 100% unplug it and it drop to something like 80% in a short time, thats a large sign that battery needs to be replaced Lastly i would say that i wouldn't listen or worry to much about apples new battery life tracker its also just a beta model and apple is never good at being totally upfront about things so just because it says 80 or 0 if the phones...
Apple is still in the 1 billon dollar lawsuit for there batteries if you take it in with this issue they will replace it for you for 30$ and potentially if theres no water damage and depending on how old it is give you a new one. MAKE AN APPOINTMENT APPLE SUCKS WITH WAIT TIME
if you didnt already change the settings in your phone to allow the computer to read the device as a media file you won't be able to get information off the device that way. Im a repair shop and depending on your skill theres a few options we do. First there are new chargers that back up devises to them like usb every time you charge it however we have never used them so I'm not sure how it works. The tried and true method we use is simply attach a working lcd to the phone download samsung data transfer and transfer all the information to a second phone. S5 lcds run about 60$ on eBay or if you go to a local repair shop they should have one in stock for you and most charge around 60$ to complete the task. Most repair shops will repair that model for 140$ just so you know. Just trying to give options.