home internet connected but no internet

Hi, this happened to me the first time I set everything up.  I don't know if this solves your issue, but just a suggestion.  On a new account they (T mobile) don't always have you internal SIM card in your tower synced up with your service.  I did a call to Home Internet tech support and they helped set up the SIM card with my service.  You can also do it yourself if you go into the modem or tower setting and see if the sim registered is the same one in your tower.  The box it came in has all the sim information on a label, it is not on the label for the tower.  Hope this helps…good luck.