For those that just disable Hamachi (either disabling the interface or the service), it's probably what most users don't want to do. If Hamachi is installed it's probably so that you can use it. :-)
So I confirm that modifying the metric of the Hamachi interface makes both of them work, the Internet connection and Hamachi.
If you want to do it automatically, you can type this at the command line:
netsh int ip set interface Hamachi metric=9000
For this command to work, the Hamachi interface should be called "Hamachi". It's what it's used on my server (Win2012).