I am getting the problem similar to this one. The weird sound keeps playing randomly and I don't know how to get it resolved in Windows 7 since Windows 7 doesn't has a dog animation in search explorer.
I think that "click" you're talking about is the "Complete Navigation" sound that happens when you visit a website in IE (though sometimes some programs use IE as a base for some of their Windows, and therefore you'll hear this clicking outside of IE too).
To stop that clicking noise:
That should stop the annoying clicking. I also suggest switching to a different browser, such as Chrome or Firefox.