Does it still browse hooked to the laptop? Hook the modem to the laptop only.
Here is a possible reason why.
Your computer has a hardware address called a MAC that never changes, and therefore uniquely identifies your computer. When your Internet Service Provider sets up your connection, they register your computer’s MAC address with their system. From that point on, your computer must identify to their system with its MAC in order to be allowed access to the Internet. Since your computer’s MAC is a unique address, any router that you might later set up as an intermediary between your broadband modem and computer(s) will have a different MAC. Your router’s MAC will be unknown to your ISP, and so they may deny Internet connectivity to your router.
What router are you using?