I dont think there is anything you can do in this situation.
If the driver for the ethernet card is installed correctly, the TCP/IP stack is installed and configured correctly, but you cannot connect to anything, you will not be able to tell if it is your ethernet card, cable or the modem/router.
The easiest solution would be to take your equipment to a mates house and use his computer to test it. Preferably a mate with a laptop with PCMCIA ports.
I would guess it's more likely USER ERROR than hardware failure.
Do PCMCIA ethernet cards show up on the Early Startup Menu? Or SCOUT?
Reinstall CNET, TCP/IP stack, web-browser etc. Use a different ethernet cable, power on / off the modem/router.
Rather than try to access external webpages, try the internal configuration webpage of the modem/router?
