ahhh ok... if the release and renew suggestions above don't work try powering the cable modem down and then backup after you plug it into the macbook. cable modems tend to lock to the
MAC address of whatever device is connected to them at powerup. if that works don't forget to power the cable modem down and backup when you reconnect it to the airport express.
i don't think its a problem with your modem persay... i think its differences in the way macos asks for an ip from the modem... are the other laptops you are refering to running another operating system?
if you really want to use wired consider getting an airport extreme base station (or even a cheapo linksys etc) ... they have the wifi and LAN ethernet ports... that way you can connect wired and wireless through the same device (and at the same time)!
be well