I had this same issue replacing my 5s battery today, after reading your comments I found that it rebooted 6 times, and then that was it. Then the battery showed 6% and did not change after being on the charger all day. So I took it apart again, and added the electrical tape to the top of the battery connector, since my replacement battery did not have the foam on top of the metal connector. As soon as I turned it back on and the battery showed 83%, it did the reboot 6 times again, so I'll keep my fingers crossed, but it seems ok now. Thanks for all the comments, they certainly helped me.