Any suggestion how to make it work?
Ask the users on the T-Mobile forum http://support.t-mobile.com/community/community what the APN settings are that you should be using.
Have you installed the SIM card for t-mobile?
This should be a no-brainier. The SIM card is either coded for one or the other. You can't have it both ways.
If you still have an old sim for Verizon, you have to install it to use Verizon data.
You can find the correct APN settings for T-Mobile on this document.