http://help.logmein.com/SelfServiceKnowledgeRenderer?type=FAQ&id=kA0a0000000shF7CAIThat's, however, german so you have to find yourself a translation.
there it states clearly, the free service is
not aviable anymore. To use the software int he future you
have to get a subscription. I don't know how you manage a free network or if you have only to get a subscription to create a network but not to get access to a network, however the Hamachi site itself states that their service is since January not free anymore and you have to pay for it.
And I don't want to scare you but you might do something very illigel right now or pay for it without knowing it (which however is very unlikely).
The site furthermore states that they suspended the free services for some reason to get a better experience for premium users.