Time Capsule isn’t being found by AirPort Utility

If the old Airport Express was connected directly to your cable/DSL modem and the new Time Capsule replaced it (again, directly connected), you may need to reboot the modem (generally by unplugging it and plugging it back in, maybe holding down the reset button) to reset its DHCP. You may also need to do this in a particular order, generally 1) shutdown Time Capsule, 2) reboot modem, and 3) restart Time Capsule.

Reason: some broadband modems seem to only assign one internal IP at a time and only check for a device on startup.

Ok, I think I understand what you're trying to do, because I've done the same. The answers listed aren't 100% accurate. If what you're saying you're wanting to do is say receive the "internet connection signal" (i.e. dsl, cable, fiber optic) from it's respective carrier & then direct it through the Time Capsule in hopes to solely extend their signal then the answers above are essentially accurate. I say essentially because based on some carriers newer router-modem combos, you CAN set up the Time Capsule in bridge mode and allow it to work as a repeater (or extend your network.) Often, with the older Time Capsules and many carriers it just becomes a pain & simply doesn't play nice all the time if you do get it to work.

It seemed to me though that wasn't exactly what you were asking to do. It seemed/sounded like you just wanted to take the signal, bounce it to the TC then to the Express. If that's the case it can be done, without any extra purchases. Certainly without any addition of a wireless jack extension, which no offense to the individual recommending it, but would be a really silly option in this scenario.

1. Place the Time Capsule next to the carrier's (i.e. I have my Uverse fiber optic modem next to my 2011 Time Capsule.)
2. Then connect the 2 via an ethernet port. At that time what you'll want to go through your carrier's step to disable the carrier's wireless signal.
3. Then allow your Time Capsule to serve as your Wireless router. You may want to go through the Air-Port Utility Set up.
4. Then connect your Airport Express & it will allow me you to then "extend" the network from the Time Capsule.

The great thing is the Airport Express offers you incredible flexibility due its portability. I know with mine I get a pretty good signal without it but with it, I can put it out on the back patio and enjoy streaming music. I have a friend who enjoys doing a movie night once a month in the summer & uses the same set-up to stream movies from their Apple TV to their projector in the driveway on to the garage. It's really cool. All the kids in the neighborhood and families get together for an old fashion block-party of sorts in drive-in movie style. All thanks to a well set up network. I hope that helps answer your question.