Cannot open database requested in login 'SharedServicesDatabase'. Login fails. Login failed for user MYDOMAIN\MyServer$

You may get an error like:

 

Cannot open database requested in login 'SharedServicesDatabase'. Login fails.
Login failed for user ' MYDOMAIN\MyServer$'. Description: An unhandled exception occurred during the execution of the current web request. Please review the stack trace for more information about the error and where it originated in the code.

Exception Details: System.Data.SqlClient.SqlException: Cannot open database requested in login 'SharedServicesDatabase'. Login fails.
Login failed for user ' MYDOMAIN\MyServer$'.

 

This is triggered by the odd fact (which I can not find documented anywhere) that the server that is housing the Sharepoint site must have its computer account listed as a user within the Shared Services database for the search to function.