The cell on charge would come up full on but die in less time than it takes to make adjustments such as many of the suggested tips: airplane mode off/on/off, reset all data, etc. Over a few days I was able to perform these functions, but the phone still went dark soon after disconnecting from charger although the battery light shows full charge. I decided to try a battery replacement.
With your explicit instructions and tools provided, the install went easily even for a novice. I had never seen the inside of an iPhone! What thrill to feel the back cover come loose (although I never saw any screws come out of the two holes either side of the power plugin). I was happy at this point even if the battery exchange didn't fix the problem. I carefully removed the two screws holding down the battery and ground wire, removed the old battery without disturbing any surrounding contacts, and inserted the new battery from iFixit. I reassembled using the new philips screws provided in the tool kit (a must unless you have a wide assortment of screws!).
And plugged in the power cord to charge the battery as suggested. In a short while, the cell lit up again as it had in the past with a too soon dead again. I was disappointed but happy that I had tried to repair the cell with a battery replacement, and was successful since the cell still worked as well as it had before. But, after an overnight on the charger, when unplugged the power connector icon along with iTunes icon appeared on the black screen. Something new! This was a big time hint that I should plugin the cell to computer iTunes site which I did. The restore software function was successful after several hours of dropping due to "I don't know what." When I left it last there was an error 3194 indicating the build was inconsistent with this software/cell phone. This is the part most will not believe: I got up during the night to check on a crockpot event and walked past a full on screen display of apps and cellular service plus wifi - no searching! I guess it was tired and needed to rest awhile before going back to work. Or, it could have been the aroma coming out of my crockpot!
Never give up - listen to the community. I had almost every symptom commented on. I'm now considering a wifi repair. If you've ever done this successfully, please let me hear about it.
Batteries Plus took in my iPhone claiming they could do it if I paid first. They apologized for not being able to successfully repair the wifi and did not refund the charge!