I was able to revive 3 iphones (5. 5s, and 6+) all presumably dead without hope, 2 had been in a drawer for some time.. I had taken each to Apple who tested and had told me logic boards were probably fried (Over the years they have replaced at least 4 phones under warranty for similar issue). I am assuming that a new battery would have had same result, but I had been told by apple that the battery was not the cause and I didnt have an extra one to try. I would suggest this as a last resort only .
1. Cut the micro usb connector off cable, strip the ends of the positive and negative wires (apple cord didn't work for me), I found it easiest to bend the tip of wire into a 90 degree or L shape
2. Disconnect the battery. You may want to remove battery from phone. Bend the cable to access connecter.
3. Quick google search for battery schematics to determine +/- pins on battery cable
4. Before plugging in position the positive and negative wires to respective pins on cable
5. Plug cable in and charge battery directly 30-45 seconds.
6 Reconnect battery to phone and push power
7. Charging or not charging symbol should appear
8. stick apple charger into port and phone should show charging, eventually turning on
All 3 phones are still working a few moths later. I had to repeat once on the 5s when it ran out of battery, but the other 2 have not had any issues since.. Good luck
Most times, Apple icon rebooting, would mean a battery issue, but only if the device was connected to a power source while the event was occurring. Perhaps, a little more detail would us figure out what exactly it is your dealing with. When you did a restore through itunes did it return any errors? any liquid damage?.
And also a lot of times specially on the 6 plus they are susceptible to have more than just LCD, as DROP DAMAGE. Good luck.
by George