Do you have a backup of your old Active Directory? All exchange configuration data is saved in the AD. You can try to make a recovery installation of the exchange server. This is a supported task to move or recover an exchange server:
I think there is no way to restore an exchange server with standard tools without having the AD containing the exchange org.
It may be possible to access the IS, even a corrupted one, with “power controls” from “Ontrack” to copy the data to an PST file. But this is a very expansive way. You can get an free eval copy to test the access on the Ontrack home page: