How can an older TC be wirelessly connected to extend an AE base?

I think the AE should be in bridge mode

That would be correct if the AirPort Extreme is connected to another router.....not a simple modem.

Are you saying that you are not able to see the settings on the AirPort Express to verify how it is configured?

Once you have the AirPort Express working correctly, it should be a quick and simple matter to configure the TC to "Extend a wireless network"

AirPort Setup in Mountain Lion will practically do everything for you automatically on this setup.

If you are not sure how to proceed, post back for further instructions.

My AExpress has the following settings

- Internet = DHCP

- Wireless = Create a wireless network

- Network = DHCP & NAT

Your original post mentioned that A cable router provides internet to it via ethernet cable.

If you have the AirPort Express configured to connect to another router....then the AirPort Express Network > Router Mode should be "Off" Bridge Mode.

If the AirPort Express is connected to a simple modem, then the Router Mode should be DHCP and NAT.

Let's get the AirPort Express configured correctly first.....then, we'll tackle the Time Capsule.

So, the first question......do you have the AirPort Express connected to a router....or a simple modem?

Start over on the TC and let AirPort Setup handle things. Temporarily, move the TC near the AirPort Express and power it up.

After the TC has been powered up for a few minutes, hold in the reset button on the back of the TC for 10 seconds and release, then allow a full minute for the TC to restart to a slow, blinking amber light.

Open Macintosh HD > Applications > Utilities > AirPort Utility

Click on Other Wi-Fi Devices

Click on Time Capsule

AirPort Setup will open up automatically and take a minute to analzye the network, then announce that the TC will be configured to extend the AirPort Express network

Enter a name for the TC device that you want to use. You can use the same device name that you used before and then click Next.

AirPort Setup will take another minute to configure the TC. When you see the message of Setup Complete, click Done

Now move the TC about half way between the AirPort Express and the general area that needs more wireless coverarage and power up the TC.

You have to let AirPort Setup do this for you, because it is configuring some other hidden settings that you cannot "see" when you try to do this manually.

AirPort Setup is also much easier and much faster than manually trying to do things.