As Steve said, Essentials will not restore from any other version.
Don't go buy Plus just yet tho. There is a free trial, and if you
cannot get converted to that trial, the purchased version is not
going to help get converted.
I don't know what will restore a Money 4.0 backup file. http://support.microsoft.com/kb/913108 describes how to convert a
Money 98 file (which would be version 6). You could try it with the
Money 2004 trial linked to in the KB article, but you might need
something older as an intermediate step.