I use sofware with NTR myself. NTRSupport specifically for helpdesk and control of Servers. I believe they have a similar product to LogMeIn for the individual PC connection.
It uses port 80 and simply required and ActiveX to install. The service is run in the cloud and requires no software on the pc you are controlling from. Firewalls are not an issue. I ended up taking over a hotel machine by accident once when I was under the impression my client was on his laptop when he said he was having touble getting into an OWA site from a hotel.
http://www.ntrglobal.com/en-GB/home.asphttps://www.ntrconnect.com/web/default.asp?