Have you removed the casing/chassis covers yet? You may want to make sure the fan/cpu is clear of dust and debri. Also check the ventilation for obstructions. Re-applying the thermal paste is the last step I would do after checking for these things.
This device is running 4.2.2 Jelly Bean which is no longer supported past 4.3. If the print feature was added to the later Android OS and/or Chrome version it looks like that's not an option.. Check out this wiki page on Google Chrome for Android.. https://en.wikipedia.org/wiki/Google_Chr...
It definitely sounds like the battery cannot charge past this point anymore. Has it ever been dropped with the cable plugged in to the port? If yes then it's possible to solder has been broken on the board.. Although the system detects power so I'm thinking it's battery at this point. Update (11/16/2017): When you connect the tablet to the pc do you see the Charging/USB options appear at the top of the notification .. try selecting the charging only option and see what happens. The PC might also not be outputting proper voltage from the port.
I assume you've removed all screws/hardware potentially holding the chassis together at this point. Next I would begin lightly prying with a plastic spudger near the outlying edges in order to see what kind of fastening plastic molding you can see.
Hey Skiebuster, in my opinion the cable or Airport/Bluetooth card itself would be the first place to start. I'd suggest opening up the rear case to expose the proper components, inspect all connections. Re-seat all ribbons and boot to test. If no improvement then I'd be willing to bet the Airport card itself has degraded over time and cannot receive the signal properly anymore.. Be aware of any sudden impacts/drops also, this would definitely cause hardware issues.
This sounds like a flow issue!!! Does the heater blow hot air? Also, you need to make sure the system has been bled of air. Excessive air in the system equals excessive pressure and the water pump won't pump coolant through the system.