Normally, this indicates an issue with your normal user account. What that is can be difficult to track down.
My first typical test is to create a new, empty folder on the desktop. Open your user account's Preferences folder and move everything from there into the empty folder so that the Preferences folder is now empty. Immediately restart the Mac.
When it comes back to the desktop, it will look like you just took the Mac out of the box. Everything, as far as the desktop is concerned, will be back at the defaults. A downside of this is lots of apps store there registration data there, so third party apps may ask you to enter your serial number again. This was part of the reason for moving the Preferences folder items rather than deleting them. If an app does ask, quit the app, find its preference file in the desktop folder you made and drag it back to the Preferences folder. Overwrite any new one the app may have created.
Yes, it's tedious, but there's no point taking the time to reinstall the OS or applying the Combo updater when a new account pretty much proves the OS is not the problem.
Edit: Before any of the above, what it sounds like is damaged is the LaunchServices database. Reset it and see if that's all that needs to be done. It's easy to do. Open the Preferences folder in your user account. Put this subfolder in the trash and restart:
com.apple.LaunchServices