It's Mika, with an A not an E.
1) Did WordPress work before you copied the DB down?
2) Did you remember to edit your wp-config to tell it that you're running Multisite? (That shouldn't give you this error, BTW, but you need to remember to do this)
3) Did you verify all the DB information to make sure it's valid?
I know I keep coming back to this, and it's for a reason.
When all sites on a network say 'Error establishing database connection' that means that somewhere, some of your information in the wp-config.php does not match what your DB has, or your DB is down. Since you seem to be able to get into the DB via localhost (MAMP comes with phpMyAdmin, so you can doublecheck at http://localhost/phpMyAdmin/), one can assume the DB is up. If the DB is up, then the issue is WP can't talk to it.
When WP can't talk to your DB, it's because
a) Your connextion info is wrong
b) Your DB is broken (try running a repair on the DB)
If the repair doesn't help, go back to rule 1. It's probably a setup issue.
You may as well go back and look at your table prefix too, but IIRC that gives a different error (it says you're not setup yet)
$table_prefix = 'wp_';
We do have directions on how to move Multisite: http://codex.wordpress.org/Moving_WordPress#Moving_WordPress_Multisite
And really that's all it is.