Suddenly you notice that you cannot access Central Administration any longer - a reboot fails to fix the problem.
First you look at IIS - CA site is there, but the 'offending' application is not.
You try to run the PSCONFIG to update and it runs through successfully, but you still cannot access Central Administration.
The problem it appears is that SharePoint gets confused and can't figure out how to enumerate the applications.
The fix is to manually delete the web application via PowerShell. BEFORE you do this, you have to make sure that the SharePoint Administration service is using an account that belongs to the farm (i.e. SP Farm Account) and NOT Local System:
If it is, change it before you attempt this (change the Log On credentials and restart the service).
Open the SharePoint Management Shell (using Run as Administrator of course) and enter the command:
Remove-SPWebApplication -Identity <URL, i.e. http://somesite;<port if needed>>
The full blown command can also be used:
Remove-SPWebApplication -Identity <URL, i.e. http://somesite;<port if needed>> -DeleteIISSite -RemoveContentDatabases
When prompted, enter Y to approve of the deletion.
For more info: http://technet.microsoft.com/en-us/library/ff607891.aspx
Be aware that this may take some time to run - several minutes as a matter of fact. If it NEVER completes, there is a good possibility that the Admin Service is still running as Local System (in that case, close the PowerShell, fix the service and retry.