Just spit-balling here I have seen this issue requiring a new front facing camera to be installed (Not just disconnected) before the issue is resolved. The fact that you got it on once would lead me to believe some form of contact issue with the battery might be involved. I have had foam get in the way of a good battery connection this can cause resetting. Possible ESD issue? Have you tried booting the phone outside of the body loose side screw could be causing some form of short.
We have seen similar issues in the past with aftermarket screens not playing nice with phones during the updating process. At one point we had to install a broken original screen, run the update, then put the new aftermarket back on. This seemed to alleviate the issue. Frustrating but worked at that time. That being said we have not seen anyone with this yet at our shop. You should contact iFixit customer service and see if they have any new recommendations.
Assuming it is just the screen assembly that needs to be replaced you should be able to find a replacement part online readily. I would normally recommend getting the part on the plastic frame if available. They are relatively inexpensive phones and screens look to be in the $40 range, this device might be more inexpensive to replace. If that is the route you take please recycle the device. How to disassemble LG K10? http://www.ebay.com/itm/New-For-USA-5-3-LG-K10-K425-Black-Touch-Digitizer-Lcd-Display-Assembly-W-Frame-/292215173602?hash=item440961b1e2:g:PKEA...
That Microphone is Soldered straight to the board near the charging port. I would check to make sure there is no debris in mic holes on frame (or case covering them) but if you are getting no sound it is most likely the microphone has failed. If its super quiet it probably has debris.