In answer to your question, yes, the ip addresses were correctly set in my resolv.conf file so I established that wasn't the issue.
I figured out (vaguely) what the problem was. I picked up on the fact that ping was using a static ip address that I had set to my second NIC (eth1). I disabled that NIC and restarted my primary eth0 which connects to my cable modem. After doing that, I had no more problems, I could ping DNS, and I was back online.
Problem solved but that still leaves me with the question as to why it was trying to use eth1 to find the DNS server instead of eth0.