Hi,
From your description, it seems that you are not able to select the tables in your database which restored from a backup file, right?
As you have mentioned, if you added the database owner in your select statement, it works well. So the cause of the problem is that the database(all datatables) owner is not dbo which is the default owner in your database. So while you are writing select statements without database owner, the system regard it as dbo.Object by default.
In your case, the system can’t find the dbo.YourObject since the owner of YourObject is other than dbo. Now you have two workarounds, first, just write the select statement with the object owner. The second way is to change the object owner to dbo.
For how to change, you may refer the following link:
http://msdn2.microsoft.com/en-us/library/ms190909.aspx
Thanks.