Will Time Capsule work on a college dorm’s WiFi network

First, connect one of the Ethernet ports of the 2Wire Gateway to the WAN port of the Time Capsule and turn both devices on, and disable wireless on the 2Wire. Your Time Capsule settings should not be changed from what they were when you had things working with your cable modem. If you've changed them, change them back now.

Then, on the 2Wire Gateway, in the "LAN" section:

1. Enable DMZ for the Time Capsule connection
2. Turn off the firewall for the Time Capsule connection
3. Set the Address Assignment for the Time Capsule connection to "public"
4. Set the WAN IP Mapping for the Time Capsule connection to "Router WAN IP address"

Then cycle power on the Time Capsule. The Time Capsule will now control everything just like it did when it was connected directly to your cable modem. Any wired Ethernet connections you add should be connected to the Time Capsule, not the 2Wire Gateway.

FYI, this works for any router or access point, not just the Time Capsule.

Your Time Capsule is not successfully connecting to the router.

1. If possible, move the Time Capsule to the same room as the router until you've got it working properly.
2. From within Airport Utility, check for software updates.
3. Connect your computer to the Time Capsule with an Ethernet cable. Be sure NOT to use the WAN port on the Time Capsule for this connection.
4. Go through the MANUAL setup and check each detail carefully. Save the configuration and let it restart, then if not working, report all settings/messages here. You should be able to see the settings still because you're connected via the cable.

EDIT: Have the Time Capsule join the existing network, not extend the network, at least as a first step, as some routers can be configured to disallow extending their networks.