After installing an Exchange 2013 Edge Transport Server (CU6) I noticed the Microsoft Exchange Health Manager was not running. When trying to start this service the following error occurred:
Windows could not start the Microsoft Exchange Health Manager service on Local Computer.
Error 1075: The dependency service does not exist or has been marked for deletion.
This is caused by an issue with the setup, where a dependency on the AD Topology services is created, a dependency that’s not possible since there’s no AD Topology discovery service and the Edge Transport server is not typically domain joined (although this issue occurs on workgroup members as well as DMZ domain joined servers).
To resolve this issue the MSExchangeADTopology dependency on the Health Manager should be removed in the registry of the Edge Transport server.
Open the Registry Editor, navigate to HKEY_LOCAL_MACHINE\System\CurrentControlSet\Services\MSExchangeHM, double click the DependOnService key and remove the MSExchangeADTopology service as shown in the following figure.
Reboot the server and the services starts again.
Note. This issue also appears on Exchange 2013 CU7.
Jaap Wesselius 
How ironic to see that Microsoft still has left unfixed to this day this with (being Exchange 2016 CU1), thanks for that gem. 🙂
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Better use command:
sc config MSExchangeHM depend=”eventlog/”
and no registry changes or reboot required.
Just do
sc start MSExchangeHM
to start service.
Admin console or powershell is required.
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‘Admin Console’ on Edge Transport server? 🙂
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