There are two ways it can be done.
1. Network the two computers together either by wireless or by crossover cable. This method will require one pc being the master.
2. Get a modem router, again wireless or cable conect.
Both pc's will require network cards either wireless or cable conect. Remember also that the bandwidth when both are online will be halved.
I see no reason why the lapton should not work with broadband. Try reinstalling the software.