No guarantee that this would solve your problems, but the chances are high if its to do with software issues and not hardware. On startup, instead of pressing the power button only, press power+home+vol up button at the same time.
You will go into a menu section where you navigate using vol buttons and home button. You will have option to wipe cache, factory reset etc. Please take note that all apps and settings will be reverted back to original. So you should back up contacts, calenders and everything you can before doing this. You will maintain your firmware update though.
Cheers