I found the answer here on the MS SQL Server Forum for Analysis Services:
Solution for: OLE DB or ODBC error:Login failed for user NT Service\MSSQLServerOLAPService error - create new login in the SQL Server database engine so analysis services can read the data in the database being analyzed.
Create login and grant access:
Open up SQL Server Management Studio [login to the database engine]>
Login (Right? click) >
New Login >add user: "NT Service\MSSQLServerOLAPService">
select the database being analyzed in the drop-down list at the bottom >
User Mapping [click on the database in the list] >
In the window database role membership click on db_datareader [this grants access to read the data]
More details here http://msdn.microsoft.com/en-us/library/ms189751.aspx
Hope this helps!
Shahfaisal Muhammed http://shahfaisalmuhammed.blogspot.com
Thank you everyone who helped me - thank you very much!