Probably you have wrong details for the DB on the wp-config.php, check the DB_HOST, the DB_USER, DB_PASSWORD, the DB_NAME and also the $table_prefix and validate if all of those details are according to the configs that you have on your PC.
If all of this is right check if your DB server is using a port that is different from the default, if it is you have to reflect that on wp-config.php
For example: define( 'DB_HOST', 'localhost:3307' ); here the localhost db server is using port 3307. You should configure your wp-config.php according to the port that your DB server is using, if it isn’t using the default one.
EDIT: I haven’t never used that plugin to do migration of websites environments.
When I need to do that I always try to do it the old fashion way.
Exporting the DB to a sql file, copying all the files from the theme/themes that I’m using, specially if it’s some custom theme, and then doing a new environment from scratch installing wordpress, all the plugins and themes and importing the sql file to the new environment.