I worked on a project that was using ExtJS heavily. I don't really know what king of problems do you actually have but we used a great combination of ExtJS, Asp.net, WCF for ExtJS Ajax calls to the server. Worked like a charm. But we abandoned the regular asp.net control usage almost completely, because most of the UI was build in ExtJS. We also used our own layout and controls with a different look and feel than ExtJS. So it didn't really look like an ExtJS app.
You could get by with regular WebMethods (as in Web Services) as well.
You will definitelly benefit a lot by using tools like Firebug and Fiddler to debug your javascript code and to examine all messages going back and forth between client and server.
Getting examples is better and better every day, since more and more people are using ExtJS in combination with various technologies. Asp.net as well.
