When I click on Quicken from the desktop, a message pops up that says "application failed to initialize properly". What does this mean, and how do I fix the problem so I can get into Quicken?

reinstall quicken and see if it clears up....
sometimes when applications are removed they sometimes disable shared resources such as DLL's

Another option is to go to a quicken forum and check their FAQ to see if there is a readily available fix.