General :: Data Takes 15 Min To Turn On After Leaving WiFi?

I recently purchased a USED S4 Active, and I am having an unusual problem with it.

I will leave my house in the morning. ALl during my drive to work, my data does't work. It's on, it just doesn't have "4g" at the top, and I can't use the internet, etc. Toggling the data does not work, neither does resetting the phone. About the time I get to work (after about a 15 minute drive), my data pops back on.

Today, at work, my phone connected to a stray wifi connection (One that I have used before, so my phone remembered it) just for a minute or two. Once it disconnected from the wi-fi, my mobile data was gone. Just like when I leave my house: It was gone for about 15 minutes, just like before, and then just popped back on like everything was OK.

I don't THINK this is an issue with my particular phone, but if it is I need to know so I can return it. I've searched high and low, but no one else seems to have had this problem. So I figured I would turn to the best!

Model: Samsung Galaxy S4 Active
Android version: 4.2.2
AT&T phone, but unlocked and working under the T-Mobile network.