Woops, missed the fact that you said you're using static IPs on the internal net. That's the same setup I have, except that I'm using a Netgear router. So the Linksys is taking care of talking to Cox, and the other machines on the LAN are working, which means DHCP vs static isn't the issue.
If you can't even ping the NIC, then it's a problem with your card's setup, not your network/internet configuration. What kind of card is it, and what module is it using?
Do you see any info for the NIC when you run ifconfig, or do you just get stats for lo? If ifconfig doesn't show anything for eth0, try ifconfig -a. The -a option forces ifconfig to list all interfaces, including inactive ones. Also, since it's a PCMCIA card, check out the PCMCIA Info page
for more on configuring PCMCIA services and troubleshooting. Sorry I can't help with that one, but haven't run Linux on a laptop yet.