It sounds like its defected. Try removing battery and holding down the power button for 30 sec then replacing battery and try powering on.
Ive never heard of this being an issue.
They can do a exchange over the phone!
they will send you a new s3 in the mail and you send that one back within a week.
if you dont you will be charged like 300$ or something. Call tmobile again tell them your issue and you cant travel 50 miles.