disconnect battery plug in screen and connect to charge. (try just the screen without the front camera) You should get an apple logo after 10 seconds or so If you don’t, check your charge port is seated correctly Sounds like your phone is fake charging
iphone batteries have over discharge protection, once the voltage goes below a threshold, the battery is locked out for safety. You can reset this but it’s better to just replace the cell with a new one. These batteries don’t “leak” so highly doubt damage to logic board from the battery
its probably damage to the modem, either from the water or physically damaged (iphone 6 bends near sim tray) Do you have imei number when dialing *#06# Do you have modem firmware under settings if either of these are missing updating will essentially brick the phone, you’ll get stuck on an activation screen. I suggest taking it to an experienced shop for repair.
Where did you get the screen, the touch panels on the copy oled, HO3 and LCD versions of the iphone X are the cheaper kind (you can see the easy digitizer in sunlight) are not very good. There was a known issue with the iphone X causing touch problems after repair and this IIRC was a software update. Try reseating the connectors and see if there is any bits of crud in the connectors on the motherboard. it could very well be just a bad screen