Re: Why can't I send a message with an attachment on my AT&T Galaxy S3 using TMobile .
Turn off Wifi. Go to Settings/Connections/More networks/Mobile networks and make sure Mobile data is checked.
Back out to the home screen, run Internet and see if you can connect to anything (like AOL or Google). If you can't, the phone is set up for AT&T, not TMobile and, since you're on TMobile, it won't work. You could add a TMobile APN, but if the phone is fairly new (it sounds as if it is), I'd bring it back to Best Buy, ask to speak with the store manager, and tell him that they sold you the wrong phone, that they were told it was going to be used on TMobile, that they were questioned what it came in and assured you it would work - and they're wrong, so would he please replace the phone with a TMobile S3.
If he refuses, just send a letter, receipt requested, to the CEO of Best Buy, explaining that it was the company's error and you'd like it corrected at no cost to you. (It seems as if some Best Buy store managers are making up rules by themselves. Most BB managers would be kind of embarrassed by the situation and make it right without anything more than an apology. But if you get a rogue one ...)
If, when you do the test with Internet and it works, there's still a problem with the APN, and they should still replace the phone. When you ask for a dozen eggs, you don't expect a dozen oranges.