Accessing a machine behind a non-configurable router
The scenario is that I have a machine in a place, and it is behind a router. The problem is that I have no access to the router and can't have this machine act as a server. This machine has servers like RSH, SSH, and VNC. When you first look at the list of servers, it would seem that it will be very insecure to allow this machine to have public access, but with help of a user here, named SpaceTeddy, I have been able to limit the number of people who can access this machine using the firewall (iptables) provided with Ubuntu.
Our goal is to be able to connect clients from outside the place with this machine. Now, it is not possible to do it the normal way, so I thought I would set up a VPN. Since we have limitations, the only software that comes for linux, that I could use was Hamachi. When I tried using Hamachi, it seemed it could not connect with its servers, when I tried going to logmein.com, it didn't work as well. One could say that either the router blocks it or logmein does.
I finally concluded that people here could help me with this. If you can please do. More than being able to SSH to the machine, I want VNC or anything that provides us with a graphical display of the machine.
One approach i thought was that I could have the machine behind router keep trying to connect to one of my machines (acting as a VPN server) after every given interval, and whenever I need to connect to the machines, I could bring up the server. This approach however needs a lot of stuff, like setting up a Dynamic DNS account for my Internet connection has Dynamic IPs, configuring the server, etc. If this is a reasonable option, please help me accomplish this.
To be more precise, the server is running Feisty, why Feisty and nothing new? For some reason I can't update the server, and installing the new version of an OS is not the option here.
Even if you have very little help do give to me, I will be greatful.