Welcome to Android Central! That sure sounds screwy. Consider a cache partition wipe as described here:
http://forums.androidcentral.com/sa...ing-into-recovery-mode-galaxy-s2-s3-tab2.html. Make sure to select "Wipe cache partition," and not "Erase data." You won't lose any important data with a cache wipe.
You could also try starting the phone in Safe Mode (
Samsung Galaxy S III - Enable and Disable Safe Mod... - Mobile Product Support Forums). If it works fine, then one of the apps you installed might be messing up the system.
If none of that works, here's a long shot. Check out this article (
Hidden Secret Codes for Google Android Mobile Phones - Tweaking with Vishal)--the 7594 code supposedly can change the power button to a shut off button, but the problem is that I can't find a code that changes it back.