It turned out to be a network adapter setting under "Wireless Network Connection Properties."  There was an "item" in the adapter's list of "items" called "Shrew Soft Lightweight Filter." When disabled this item, DNS started working again.  Shrew is my VPN client.  I don't know why it worked for so long and suddenly stopped, but this filtering was the cause of my DNS issue.
I am running Windows 7 Pro.  My internal wireless card stopped working recently.  It had been working for months.  When I let IE "diagnose" the problem,  I get the diagnosis of "The DNS server isn't responding."  I have tried many things:  1.  I have reproduced the problem at work and at home.   It is NOT my router/modem/ISP. 2. No other computers are experiencing the same issue. 3. If I plug in a USB based network adapter, it works fine. 4. It is strictly a DNS problem because I can type the IP address for www.google.com and get the webpage loaded. 5. I have tried "hard coding" the DNS server IP address. I have tried my ISP's DNS servers as well as the public domain google DNS servers (8.8.8.8 and 8.8.4.4) 6. I can ping the DNS server, but nslookup fails. 7. I have tried turning off the windows firewall and the virus software. 8. I have updated the driver, and I have even uninstalled/reinstalled the wireless network card Strange. Something is blocking this particular wireless card from receiving DNS responses. Any ideas?   Thanks!
Inspiron 1764 - Internal Wireless (1520) - DNS isn't responding