When you connet the modem and computer do you get a light on the card itself (probably right next to where you're plugging the cable in)?
I would imagine you should also get a light on the modem to say that it's connected via Ethernet (have to confess that I don't have a cable modem so I can't say for sure).
Have you tried a different cable?
If you go to Start > Control Panel > Network Connections can you see if the network connection in there is enabled/disabled? Also have a look at the 'status' and see if you're getting an IP address when connected to the modem.
I would also try pinging the modem when it's connected. Start > Run > CMD. Type:
And hit enter.
The problem is that I can't remember what the IP of the modem should be

, hopefully someone else will be along soon who can tell you (and possibly offer some more advice).