I have an iPhone 4S Verizon?

So as it says I have an iPhone 4S Verizon that is 6.0.1 unlocked by a gavey SIM card it's unlocked to tmobile it works fine but there's a problem the Internet does not work the tmobile Internet that I get from them doesn't seem to work I don't know why can someone please help me?

Check the APN (found under settings), and verify that it is correct for T-Mobile. If not, then edit the APN.

As the other answerer suggested check the APN settings. I'll add, because of different frequencies between the iPhone & T-Mobile you may not get 3G & be limited to EDGE (2G).