Installed WS on my work lappy (Vista business x32) and it works fine, so I'll try and run a trace with that tonight.

Which ports and protocols does LogMeIn Hamachi2 use?
Hamachi2 uses several ports to achieve connectivity to the mediation servers, and to peers.

Server Connectivity
TCP 12975 (initiator port)
TCP 32976 (session port)
If the above ports cannot be used to achieve a connection, Hamachi2 will try again using SSL (TCP 443).

Peer Connectivity
Peer connectivity has several methods and ports.  By default, Hamachi2 will broker a peer connection over UDP.  UDP uses random ports by specification, so it is not possible to open a single port for peer connections for UDP.

If UDP direct connectivity cannot be established, Hamachi2 will try to initiate a relayed UDP connection.  This is done with the target of:

UDP 17771 (relay connection port)
If UDP direct and relayed methods fail, it is somewhat unlikely that TCP connectivity will work, however, Hamachi2 will try it.  In some environments, a hardware firewall is used to block traffic on specific ports, but not protocols.  As such, Hamachi2 will try to broker a connection between peers over TCP 443 (non-SSL)

And lastly, Hamachi2 will try a relayed connection over TCP 443 (non-SSL) before giving the user a message that the peer is unreachable.

 Note:
TCP peer connections are very unlikely to be successful in cases where UDP connections would not work, because the triggers for them not working are the same (router issues, improperly configured NAT, multiple NAT devices on both ends).
Additional Notes
You can set a static UDP listening port by configuring it in Preferences > Detailed Configuration, but note that this will require you to forward that port's UDP traffic from your router to the machine, if you are behind a router.  Note that this port isonly used for server communication.  Also note that if you have multiple machines to do this on, you will need to choose different ports for each to avoid conflicts.