casemod:
No, I am looking for either a program to do that (even if using a single chip for that) or how to activate the TCP stack available on the phone itself.
I expect your phone/modem will provide an extended AT interface. In that case you can use the AT interface to go through the steps needed to activate the PDP context. Look for the data sheet for your modem, or Google 'at gprs' to get a general explanation.
If you want something to do all this for you, you would need to locate an AT client library that encapsulated this logic and covered the features you want to use. I don't know whether that exists for Arduino GPRS using the command set supported by your modem. Ultimately somebody has to write these things, and that somebody might need to be you.