Here's what I get when running MYBACKUP from my admin and appending &debug=ON to the end of the URL:

Checking Path: /usr/bin/
COMMAND FILES SELECTED:
mysqlexe="/usr/bin/mysql"
mysqldumpexe="/usr/bin/mysqldump"
COMMAND: "/usr/bin/mysqldump" "--host=localhost" "--user=earnest3_Admin" "--password=XXXXXXXXXX" --opt --complete-insert "--result-file=/home/earnest3/public_html/admin/backups/db_earnest3_zen139d-20100622180548.sql" earnest3_zen139d 2>&1
Result code: 2
valueA: mysqldump: Got error: 1045: Access denied for user 'earnest3_Admin'@'localhost' (using password: YES) when trying to connect
valueB:
0 => mysqldump: Got error: 1045: Access denied for user 'earnest3_Admin'@'localhost' (using password: YES) when trying to connect
Failure: The database has NOT been saved.
Know that your mod (v1.3) worked fine in 138a. I don't know that I've changed anything other than just installing your v1.4 of the mod into 139d. My hosting service does offer ZC through my Cpanel if I want to install it through them but not being sure what version of ZC they were using I did a manual ZC install, having done it several times before. It may very well be something my host may have to tackle.

Thanks...