Yes, I have root access.
Never mind though, I just figured what was going on. Just in case if anyone else has this problem:
For Ubuntu and Gnome change the line "DisallowTCP=true" to "DisallowTCP=false" in /etc/gdm/gdm.conf or use gdmconfig to deactivate the setting "Always disallow TCP connections" for the X server.
More detail:
http://www.xskat.de/xskat-lan-irc.html
a) Configure the X servers to listen for connections on port 6000.
The X server has to be started without the option "-nolisten tcp". Sadly this has to be done quite differently depending on OS and display manager.
For SUSE and KDE set DISPLAYMANAGER_XSERVER_TCP_PORT_6000_OPEN to "yes" as root using the /etc/sysconfig editor in yast2 under "Desktop -> Display manager" and execute SuSEconfig afterwards. You may have to comment the line "ServerArgsLocal=-nolisten tcp" in /etc/opt/kde3/share/config/kdm/kdmrc with a "#" at the beginning of this line. Also, there should be no option "-nolisten tcp" in /etc/X11/xdm/Xservers.
For Ubuntu and Gnome change the line "DisallowTCP=true" to "DisallowTCP=false" in /etc/gdm/gdm.conf or use gdmconfig to deactivate the setting "Always disallow TCP connections" for the X server.
Logout and restart the graphical user interface then. If executing the command "netstat -an|grep :6000" gives some output, the X server is listening on port 6000.
b) Disable firewall for port 6000.
If a firewall is protecting against other LAN hosts, at least port 6000 has to be opened.
Don't open ports for connections from the internet!