Aren't the Airport and Ethernet Network settings independent from each other? That would lead me to believe the problems are unrelated, or at least not directly associated. For it to be a problem with DHCP, both would have to be configured incorrectly (unless it's at the router level).
It could be a problem with your router (perhaps the wrong settings), but that doesn't explain both problems unless you have a wireless and wired router.
My original though was DHCP though.
...OK, I don't think I proved anything. 😱