I was having the same problem - from the moment I received the email from Telstra informing me of the successful move to the new system, I received no emails. I could send emails, not receive.
Having spent over an hour on the phone with a person from Telstra Support, he discovered that the new system had automatically selected/enabled auto-forward with no destination ("Settings" "Mail" "Auto-Forward").
Having unchecked the box, emails have started arriving in the Webmail and Outlook Inboxes.
Unfortunately, any email sent between the notification and the resolving of the problem, has been lost.
MacG