I have a dedicated PC with Debian Linux and now wish to install Oracle 11gR2. All the required changes and settings were made as per Oracle Pre-Install.
When I start the installer it errors out almost immediately due to a display problem as it it verifying if the display can accommodate 256 colours. The /etc/hosts file has a setting: 127.0.0.1 localhost so I set the DISPLAY=localhost:0.0
But it fails, why?

Probably a combination of reasons. First, the IP address shouldn't be your loopback address, but the IP of your machine itself. Second, you need to make sure that your X display manager is accepting incoming connections. At a prompt, type in "ps -ef | grep -i listen". If you see something like:
then your X server isn't accepting incoming connections. Note the "nolisten" argument. There are many how-tos on how to let Debian accept incoming X connections, and this has been dealt with on this site many times as well...give a quick search, don't want to type up the same thing again.

Also, since you're paying for Oracle support, you can get help from them.

Apparently the problem is with Debian. Here is the case... The initial user (say user A) logs into the OS and is granted all the capabilities of graphical display and xterm. 'xclock' works. If I 'su' to another user (say user B) then that new user, for some reason, does not inherit the graphical capabilities. 'xclock' does NOT work. Now if I log out and login as user B everything works fine. As soon as I 'su' to user A then user A does not have the graphical capabilities !
But the root account always has the graphical capabilities go figure !

No, that's not a Debian problem, but rather that the DISPLAY environment variable is getting clobbered when you su to another user. If you log in as user A, and look at the variable, then 'su' to user b and set it to be the same, things should work just fine.