No guarantees, but this occasionally does help someone with a similar problem. Take the battery out and leave it out for a good half hour or more. Overnight even better. Put it back in and test it.
If it doesn't work, maybe the power switch inside has completely gone bad. Under warranty or not?
Sent from my Sprint Samsung Galaxy SIII on TouchWiz 4.4.2 with Wicked X v6.5, Ktoonsez' latest kernel and the latest Philz Touch Recovery.