Applejack is a good tool for Snow Leopard, but it won't diagnose any problem. Applejack is run from single-user mode and, if I remember correctly, will allow you to repair your startup disk without needing to boot from an optical disk or alternate drive.
From Applejack you can also delete certain cache files and repair permissions.
The spinning wheel could be caused by one or more of dozens of issues.
First, try this: create a new user account then log into that account and see if the problem exists.