Yup, Hamachi is one of the common ways to lose your Internet connection and has been for many years.
There are many fixes, but here is a quick one that has worked for me and others:
Run an elevated command prompt window by selecting it with a right click and choosing run as administrator
Run a "route print" and then in the interface list find the leftmost number for the line that corresponds to the Hamachi network interface. Lets call that number xx.
Then run "route delete 0.0.0.0 IF xx" (where xx is the number from the route print that represents the Hamachi network interface above).
That should allow you to connect again.