Hi,
Just had the same problem as you! ;) Well, here's your answer!
To solve it:
1.Press Windows+R. (It will open a little window called ''Run)
2.Write -> services.msc
3.Once the window called ''Services'' is open, search for LogMeIn Hamachi Tunneling Engine
4.When you found it, right click on it and click on ''Start''
5.After it started and the Status is now Running, right click and click on ''Properties''
6.Go to Recovery
7.Change all the place where it's write ''Take No Action'' to ''Restart the service'' (So, you'll have to change First Failure, Seconde Failure and Subsequent Failures)
8.All done? All right! Start Hamachi normally, and go on for your activities! :D
Have a nice day,
-Pitivier24, a simple Hamachi user :p