I know that if you try to set up a network with Gigabit equipment, and then have a device that only runs at 100BaseT, it slows the whole network to that speed.
So hypothetically speaking, if I were to right now upgrade my equipment to Gigabit, would it run at Gigabit speed, or would the broadband modem slow everything down? I really haven't seen any new broadband modems that state it is compatible with 1000BaseT, but I don't really know if that would play into the equation anyway.
Your Internet speed will always be limited by how much your line allows for download. It's unlikely you will reach the same speeds on your Internet connection as you will on your LAN network - there's too many factors involved outside of your own network, let alone within it. If you have a router, it will need to be compliant with the speeds as well - your modem isn't really part of your LAN network.