Try one more time before you take the Time Capsule to the Apple Store.
First, power off the modem completely by pulling the power cord from the back of the device. If the modem has a battery that is easily accesible, remove the battery. Disconnect the Ethernet cable from the modem as well. Leave the modem powered off at least 30 minutes.
Perform a Factory Default Reset as follows on the Time Capsule:
Pull the power cord from the back of the Time Capsule
Wait a minute or two
Hold in the reset button first, and keep holding it in for another 10-12 seconds while you simultaneously plug the power back into the Time Capsule
Release the reset button after the hold period, and allow a full minute for the Time Capsule to restart to a slow, blinking amber light
Power off the Time Capsule again
After the modem power down period, reinstall the modem battery if it was pulled before.
Connect the Ethernet cable from the modem to the WAN "O" port on the Time Capsule
Power up the modem and let it run for 15 minutes
Than, power up the Time Capsule and let it run for 5-10 minutes
Open up AirPort Utility
Click on Other WiFi Devices
Click on Time Capsule
Follow the guided setup and prompts. It may take a few minutes for the light next to the world in AirPort Utility to turn green.
If you still cannot get an Internet connection on the Time Capsule, try another Ethernet cable. If still no luck, take the Time Capsule to an Apple Store or Apple Servicer to let them have a look.
If the Time Capsule works at the store, then you know that the Time Capsule is working correctly and you will need to focus on the modem or the Internet connection from your provider.