Using Airport Extreme as Wireless Extender for Internet-Connected TV

Hi. I'm trying to make an Airport Extreme work as a wireless connection for the Internet features of both my TV set and my TiVo box (a Viera with Internet connectivity, and a DirecTV HD TiVo).

I was successfully able to use an old Airport Express for this, by setting the Express up to access the wifi network originating from my Time Capsule, and then connecting an Ethernet cord from either the TV or the TiVo straight to the Express. Worked beautifully in both cases; I was able to use the automatic network setup on each device, and it just started working.

But I want to connect both devices at once. Rather than buying a second Airport Express and plugging them both in behind my entertainment center, I decided to buy an Airport Extreme. I figured that it had multiple Ethernet ports so I could plug in both devices at the same time, and I'd be able to use the Extreme like an Airport Express.

But it's not working. Neither the TV or the TiVo can successfully make a connection through the Airport Extreme. I'm able to successfully configure the Extreme, and I set it up as a wireless network extender; it can successfully connect to the wireless network generated by my Time Capsule and is generating a green light. I plugged an Ethernet cord from the TV and another from the TiVo into the Extreme. But the two entertainment devices are unable to connect -- if I use the devices' automatic network setup, the devices don't seem to be able to get an IP address from the Airport Extreme. I then tried going into each device and manually entering the Airport Extreme's IP address, subnet mask, etc. This time one of the devices got a little farther in the connection process; it acquired and verified the IP address, but then gave a message saying that though it identified a home network, "the gateway doesn't respond".

Any clues what I'm doing wrong? I recognize that this is an unusual use for an Extreme, but it worked so well with the Express. Should the Extreme be set up in Bridge Mode instead of just as a wireless network extender? Do I have to toggle some setting on it to allow devices connect via those Ethernet ports?