Sounds like a software problem not a battery problem. Try putting it into Recovery Mode.
Turn off the phone, connect phone to computor, Then turn off phone and then hold down powerbutton and home button untill the "connect to itunes logo" appears then on the computor, reinstall it and it should work.
Turn your iPhone off by holding down the sleep/wake button (on the right side on iPhone 6 and up, on the top corner on all other iPhones). Hold until the slider appears at the top and then swipe the slider. If your phone doesn't respond, hold the sleep/wake button and the Home button gether until the screen goes dark (on an iPhone 7 series, hold volume down instead of Home) Connect your iPhone to your computer. If you don't have a computer, you'll need to go to the Apple Store or borrow one.
Perform a hard reset on the phone. Do this by holding down the sleep/wake button and the Home button at the same time (again, on iPhone 7 use volume down). Continue holding for at least 10 seconds. If the Apple logo appears on the screen, keep holding.
Let go of the buttons when the Connect to iTunes screen appears (it's the image of the cable and iTunes icon shown at the top of this article). The phone is now in recovery mode.
A window pops up in iTunes offering to let you Update or Restore the phone. Click Update. This tries to resolve the problem without erasing your data.