My buttons are broken and my phone is locked how do I turn it off and turn it back on again?
Let the battery die, that will shut down the phone. Once dead and off, plugging the phone in to charge will turn it back on. This is assuming both the power and home buttons do not work.
Try plugging it into a new PC when it asks Allow/ Disallow, it definitely come to slide to unlock screen, then go to Settings>General>Auto-Lock>Never.
Simply manually disconnect the battery by removing the two bottom screws and then lifting the screen.
Once screen is up, unscrew the 3 battery connector shield screws and then disconnect battery flex. Re attach when ready