So the desktop is working fine, but on the laptop you are getting the error.
the error points to a problem with the database connection.
Open the Dreamweaver Database tab (Window -> Database) in the list of connections, double click your connection, then press the test button, does the connection test pass or give an error?
In the connection window, for the database, press the select button, does this give a list of databases?
you may have to recreate the database on the laptop computer.