I believe I have identified your problem. You modem has a built in router. It can support up to 64 computers via a hub or switch.
Look at the section titled Features
. Refer to bullet point number 5.
What this means is you have one of several choices.
1. Buy a hub or switch.
2. Keep you current router, the Linksys, and bridge it which means you are going to disable the router feature and use it as a hub\switch.
3. Bridge the modem's router function. This is what I would do. Contact your ISP for instructions.Scientific Atlanta DPC2100 Series Cable Modem