Cuddles

Just clutching at a few more straws for you.

Do you have a program called pump on your system?
There should be an executable file called /sbin/pump.

If so, then you could try simply creating a regular file called /etc/resolv.conf, making sure the permissions are 644.

If you recall, you currently have a symbolic link at /etc/resolv.conf, pointing to /etc/dhcpc/resolv.conf. Perhaps you should first rename (using the mv command) the symbolic link to something else to keep a backup copy.

Do all of this before you connect to the internet.

After you connect to the internet, check to see if the new /etc/resolv.conf file contains a nameserver ip address. If so, then try to dig something as cuddles.

OK, a summary of steps for you (first lot done as root).
mv /etc/resolv.conf /etc/resolv.conf.keep
> /etc/resolv.conf
chmod 644 /etc/resolv.conf
dial the internet
cat /etc/resolv.conf
then as cuddles
dig www.knoppix.net

If this works, great.
If not, you can put everything back as it was by
rm /etc/resolv.conf
mv /etc/resolv.conf.keep /etc/resolv.conf