Absolutely not. You WILL need the "Linksys box" (router) and the broadband modem (the thing you got from SBC).
There are a series of "ports" on the back of the router. ONE of them is designated for the modem. You see, instead of the modem going straight from the wall socket to the computer, it will instead go from the wall socket to the router in its designated port. Then your computer will plug into the router.
Single computer setup: Wall - Modem - Computer.
Multi computer setup: Wall - Modem - Router - Computers.
The thing is, even though you will have TWO computers on the network, one will be wireless... so in the back of the router, you would generally have JUST the desktop plugging into the router. The laptop would not connect with any type of hardwire... because as I said, it's wireless.
I hope this helped some. There are tons of diagrams on google if you need assistance when it comes time to hook everything up. Check it out.