Since it appears to be a log on failure between ssas and sql, check what account the analysis services service is running as and then verify that the sql server has a log in for the analysis services service account and that this log in is in the db_reader role for the sql database.
Also if the ssas server and sql server are not the same machine then there is a firewall port that would need to be opened on the sql box to allow connecting to the database from another server. There are articles on the port settings needed for ssas on msdn if you need that.
Hope this helps,
Lance