I don't have my 6811 anymore, I got it traded for a 7422, but I don't recall there ever being a LAN LED on the 6811 and I don't see one on this model either. I didn't explicitly look for it on the 6811 so I might just be talking out my tail here too.
If the XP firewall is turned on, it blocks ICMP traffic by default. Reconfigure or temporarily disable the firewall on both source and destination computers before you try pinging.
Here is the process I use to troubleshoot TCP/IP issues, ignore anything that doesn't apply to you, I'm putting in all steps in case someone else wants to use this as a template:
1. Ping 127.0.0.1. This should work with or without a network cable. Successful results tell you that TCP/IP is properly installed and the local firewall is not blocking ICMP traffic.
2. Run IPCONFIG /ALL. Note your own IP address. If it is 169.254.xxx.xxx then you are configured to obtain an IP automatically but unable to contact a DHCP server. Otherwise, note the address of the DHCP server, the default gateway, and at least one DNS server. It is a good idea at this point to first run IPCONFIG /RELEASE, then IPCONFIG /RENEW. If you don't, then most of the rest of these steps could be misleading. A failed /RENEW could indicate that you have no network connectivity at all.
3. Ping your own IP address, even if it is in the 169.254.xxx.xxx range. This requires a network cable to be attached from this device to another. If this ping is successful, then your network cable and card are at least mostly good, and you can communicate on a network. If this does not work, then either your card, your cable, or the device you are attached to is bad. Try another port on the switch/hub you are attached to, then try another cable. If you are still unsuccessful, it is either the switch/hub or your network card.
4. Ping the default gateway. If you have gotten this far and are still unsuccessful, the problem is beyond this machine.
5. Ping the DNS server(s). If this is unsuccessful, it may just mean the DNS server(s) don't accept ICMP traffic, or they are down. You will be unable to resolve host names to IPs, but standard IP traffic will work.