My cousin has a SGS3, which suddenly started showing the power options screen (when you long press power button). Now his phone restarts on its own every time. When you insert the battery, it turns on by itself. If you try to access download mode or recovery mode, it does it but restarts again. I read it may be the power button is not working properly, but I dissassembled the phone and the switch is works normally (it's not broken, either stuck). I read several solutions about clearing cache and stuff, but it just keeps restarting! Like if someone were pushing the powerbutton every time. Btw, he discovered he can turn the phone on and actually stop the phone from restarting if he continously presses the power button and menu button alternatively without stopping (which is useless). When he stops doing that, 3 secs later, it restarts again. Any suggestions?