This could possibly be due to having the Registry Key for Password Manager Logging enabled in a previous installation of Password Manager on the same Server. Uninstalling Password Manager deletes the Logging Folder but doesn't revert back the Registry Key. Once the new Password Manager Service attempts to start it hangs because the Logging Folder is not present.
The following Defect ID was created to resolve this in a future release of Password Manager:
274716 - Logging Issues With PM AD and ADLDS - Service hangs if the log folder doesn't exit, uninstallation doesn't remove the Registry Keys
Delete the Registry Keys for Password Manager Logging and the Service should start.