I had a similar problem after upgrading Windows 7 and 8.1 to Windows 10 where the service was stuck in the starting state. As a software engineer I've had lots of experience with services. Logmein depends on the Windows Management Instrumentation service. I changed the dependencies to add Workstation and this fixed it. To do this open a command prompt in administrator mode and enter the following
sc config Hamachi2Svc depend= Winmgmt/LanmanWorkstation
NOTE there is a space after the = but not before it
Sorted!