LocalSystem has extensive privileges on the local machine, while LocalService and NetworkService have minimal privileges. Thus, it is very similar to the fact that your service needs some privileges that are not in the LocalService . As marc_s notes in his comment, the first step is to check the event viewer to see if there are any relevant error messages.
If this does not help, try adding some exception handling from the startup code to the service and log all exceptions from the Event Log, I hope this gives you enough information to find out what it is. this requires higher privileges.
Hans olsson
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