No Network Adapter Found?

Just to add to the above I'd seen nothing but problems when installing/uninstalling Hamachi (my Brother had it installed once and had a similar problem to you).
 
I would make sure Hamachi is fully uninstalled, using Revo Uninstaller (download free version) it should get any remaining bits probably from the registry - http://www.revouninstaller.com/revo_uninstaller_free_download.html
Restart after doing this and see if there is any change.
 
If you want to check whether the adapter still works and isn't damaged look into trying it in another PC if you can (just to see if it is detected and default drivers installed on other PC).