If you had only disable the AD Object but no the mailbox this one still operational and the only way to search email history is getting access by OWA (if the service was enabled for the mbx) now if you also disabled the Mbx I'm affraid you are not getting any mail.
- you could grant yourself rights to the mailbox and then view it via Outlook and here are a few links that can help https://technet.microsoft.com/en-us/magazine/ff381460.aspx and https://technet.microsoft.com/en-us/library/Aa996343%28v=EXCHG.141%29.asp
- Or use a 3rd party product like Lucid8's DigiScope
http://www.lucid8.com/product/digiscope.asp that can access the mailbox forensically from the Production server or from an offline copy of the DB that holds the MB
Disabling the AD account means that the user cannot log into their email but email can still be delivered to the mailbox and you can also grant yourself rights to add the mailbox into Outlook. To do this, use the below command:
Get-Mailbox mailboxname | Add-ADPermission -User admin -AccessRights FullAccess
More info here: https://technet.microsoft.com/en-gb/library/bb676551(v=exchg.141).aspx
Let me know if this helps you out or answers your question.
Thanks.