It sounds like you may have set up your Time Capsule to "join" an existing wireless network. If that is the case, the Time Capsule will only perform as a wireless hard drive, and it will have no routing ability at all.
That is why the Ethernet ports are not working. They are not enabled when you configure the Time Capsule to "join" a wireless network.
If you want to enable the Ethernet ports on the Time Capsule, you will have to Hard Reset the Time Capsule to get it back to original factory default settings and then set it up again.
The critical element here is that the Time Capsule must connect to your modem or modem/router using a permanent, wired Ethernet cable connection. Connect from the modem to the WAN "O" port on the Time Capsule......just like you see in the Setup Guide....... and then set up the Time Capsule again.
If you need help with this, we need to know what operating system that you are using on the computer that you use to administer the Time Capsule.