In my case I had to delete the services in my installshield project and start from square one. My original service components were added manually and I couldn't get them working, the only error I was getting was the same "Error 1920 service failed to start. Verify that you have sufficient privileges to start system services." that you were getting. After deleting my components, I re-added them using the component wizard.
I actually had to create two new components. One was of type "Install Service".
The other component I had to add was of "Control Service" type.
I had to choose the service that I had setup when I added the Install Service component.
After that it worked, even though nothing looked differently from the components I had added manually. Installshield must do something behind the scenes when it wires up the service components with the component wizard.
All of this was with Install Shield 2016.