If the SIM card works, and you can get a network signal, then the deice is unlocked and it is a different error that is stopping internet from working.
It could be due to a number of reasons that internet isn't working, I am going to list them:
APN (Access Point Names) allow your device to connect to mobile internet. You nust ensure you have the correct ones installed for your network.
Device not compatible with internet system
IIRC, the T-Mobile US network uses a different system... It could be that this system isn't compatible with your Indian network for internet access.
Other than the above, I cannot think of any reason internet wouldn't work when mobile network does. Make sure your network is letting you use the internet (no bars, you have internet with your plan) - otherwise, I do not know.