If not then that seems like the main part of the work because once you have that then you can download everything else.
Unless it was already in BIOS or some network hardware remote admin Intel thing and there was a way to hack into that to use it. Then you would not have to implement TCP IP.
To me the question is what is the minimal part of TCP /IP that you would need. I guess also you need ethernet if that's not in the C libs.
To cheat maybe your computer has a modem and there is a BBS - simpler protocol.