Maybe the new AirPort base station is broadcasting its own network separate from the one being broadcast by the Linksys routers. In your Applications folder, go into the Utilities folder and open AirPort Admin Utility. Select the AirPort Extreme and open its configuration window. (Now, I don't have Leopard yet, so I don't know what's changed since Tiger and what hasn't, but...) Find a drop-down menu in one of the tabs that lets you switch the AirPort Extreme between creating its own wireless network, or joining an existing one, and select the latter. (You'll probably have to fill in the network's name and password.) After saving the changes you've made and allowing the AirPort Extreme time to restart, it should start simply extending the range of the Linksys routers' wireless network. Hope this helps!
Three years of adventures with an AirPort Express, may it rest in peace ;)