Battery shows charged but will not keep phone on
Trying to use a 1st gen iPhone. When I got it the battery was dead. Charged it fully. Icon reads full or on AC power when plugged in. However, when I pull the ac power, the phone will not sustain power. Oddly, if I toggle the lock/unlock button, turning the screen off and on, it seems to stay on indefinitely. But if I let it sit, even a minute or less, it will not come back on until I plug it in. When I do, the batter still shows full power or AC power. I have done a full restore and update. So it's charging. Running on AC power. Running battery power as long as I'm using it. Even took the auto lock off for 5 minutes. It stayed on. But if it sits on battery, it will not come back on.
I would definitely start with replacing the battery. iPhones do weird things with bad batteries. Here is the guide, and I am sure you know it's a bear of job. The battery is available here iPhone Gen 1 Replacement Battery Hope this helps, good luck.