You should focus on simply connecting the Wii to the Linksys router via the LAN adapter for the Wii. This is the simplest and most straightforward setup, so if you can get that to work then you can move on to wireless.
I am not surprised that connecting the modem directly to the Wii wouldn't work. Most DSL modems are configured to bridged/passthrough mode where the computer (or router) are expected to handle the PPPoE login.
You might want to try temporarily disabling your laptop's wireless and try using the laptop on the exact same network cable you're connecting to the Wii. That will tell you if it's the Wii or something with the cable/router.