Checking the firewall is really the only suggestion I have at this point. Firewalls tend to block file sharing over newly added adapters if they were marked as public to begin with, and will not revert this setting when the adapter is trusted.
One firewall that can be particularly tricky is the new Norton Internet Security, or Norton 360.
In that firewall, you will want to go to the Tasks section, and choose Network Security Map. This will enable a very usefull feature (as far as I am concerned) and will allow you to trust the network adapter itself.
By default, Hamachi does not dictate what can and cannot be sent over it, so out of the box, you should be able to do anything that your Firewall and OS allow you to.