Thanks.
I didn't have to enable those ports, only the one for Echo request and then it worked fine.
So to summarize my problem: the Diagnostic Tool complains about the driver, but the problem seem to be the Diagnostic Tool (it still complains). The problem I had was the Hamachi network that was first created. When I deleted that and created a new I could see the other computer in the network. Configuring the firewall correctly and then I could get the computers in the network connected!