Ideally you'll touch base with your new support contact - external db connections often require changes to firewall ports, and sometimes extra drivers on the web servers depending on which db type you're connecting to.
But - few things to try...
set "debugauthdb" to "yes" on the external db authentication settings page.
Look at the scheduled task logs for the auth_db task..
On the list of scheduled tasks click the task logs icon beside the auth_db task (it's the icon to the right of the cog on the task)
then click the magnifying glass icon on one of the auth_db task runs and see if any useful errors are reported in the log.
But - few things to try...
set "debugauthdb" to "yes" on the external db authentication settings page.
Look at the scheduled task logs for the auth_db task..
On the list of scheduled tasks click the task logs icon beside the auth_db task (it's the icon to the right of the cog on the task)
then click the magnifying glass icon on one of the auth_db task runs and see if any useful errors are reported in the log.