I dont like to assume anything so i have to ask, did you try another lcd? I didn't see if you mentioned whether you did or not. Also Im curious what temp do you use to remove the touch ic's. Ive been starting with 270 to get them off then 240 from there on out. Never had an issue with anything else getting damaged and I dont use tape or heatsinks to protect the other chips.
If the battery will not hold any charge whatsoever, and the laptop only runs off the charger then theres a chance you may be having a logic board issue or a battery issue. How was the battery working before it stopped working? Did it get worse over time or one day it was normal and the next day it was dead?
The digitizer usually only affects the touch function, the LCD is what shows picture so it kinda sounds like thats what your having an issue with if the picture is distorted or irregular. Also where you are putting pressure happens to be about where the LCD plugs into the logic board. There is usually a metal shield over that connection to prevent it from coming loose so its tough to say what happened for sure until you open it and look under that shield. If everything is connected properly you may need to replace the LCD.
Have you checked voltage on the battery? Maybe the new battery was junk and died already, especially if it was an ebay part. Use a multi meter on the outer pins of the battery connector. Report back what you find.
Missing a screw shouldn't cause that. The phone has 2 mics and the one your having an issue with would be the one on the bottom connected to the charge port. Its right in between the charge port and headphone jack. Make sure the flex cable coming from the charge port is secure to the logic board. If you can open it and just reseat the connections and make sure the mic is in place properly. Also look for damage around the charge port area, there are some small components that could get damaged but thats less likely. Sometimes the mesh on the bottom covering the mic can get clogged but I dont think thats your issue.
I seen that you tried charging it from a ps3 and a pc. Your tablet needs a 2amp charger and will not charge normal from a usb port. Try this first, you will see the battery with the lightning bolt until the battery reaches about 3.7v and will register 1% then you will see the animation with the battery filling up. I have also seen a bad charge port cause this as well as cold solder joints on the battery connector.
Look for advanced repair options and see if you can get into system restore, if the problem is software you can revert back to an earlier time before install the AV and keep all your stuff. To me it sounds more like a hardware failure like maybe a hard drive. Your pc likely has some built in diagnostics that you can run to check the hardware. If you just reinstall Windows without checking hardware it could fail again.
Sounds like the lcd is broken. I guess theres a chance it could be the connector or logic board but all the phones like yours Ive seen with that issue it has been the lcd. Usually happens after a fall or coming into contact with liquid or moisture even if it was days before. You could open it for inspection but if everything looks ok then the only way I know to find out is to hook up another screen that you know is good.