Check that you don't still have the DNS server entry hard coded in the settings for your wireless connection, via the Control Panel -> Network Connections -> right-click it then select Properties -> highlight Internet Protocol TCP/IP then click Properties. Make sure that you're using Obtain DNS Server Automatically.
---------- Post added at 00:44 ---------- Previous post was at 00:41 ----------
The Eclipse DNS server is most likely configured to not work for non Eclipse customers, and when it realises you've not got an Exlipse-assigned IP address, I'd guess it ignores you from then on.
At a guess, I'd say that the applications that are working are relying on using the IP address instead of domain names, so they won't need to perform any DNS queries and can connect fine. You'd probably find you could browse the internet fine, if you knew the IP addresses of all the sites you want to visit instead of using the human-friendly domain names
