You should use full stop and comas in your sentences, because your last post is totally not understandable for me.
If you only want to start this one application without password prompt, then I can give you solution which I use to start an XBMC on my secular parents media center PC, there are several approaches, I choose this one. You did not specified which Ubuntu version you use, I assume the latest. Basically you need to add file "/etc/init/tty1.override" to start your application instead of usual "getty", for example:
start on stopped rc RUNLEVEL=
stop on runlevel [!2345]
exec xinit -- /usr/bin/your_application
Look in /etc/init/tty1.conf for orginal file. Leave other tty?.conf entries for maintance (available after pressing CTRL+ALT+F2, 3, 4, etc.) and disable display manager, by backing up somewhere or creating appropriate empty "*.override" file (I didn't test this), it will be "gdm.conf" or "kdm.conf" or similar in the same directory. After that steps, when computer boot up, it will start your application. Depending on functions in your application you can control its respawning, by deleting or leaving alone "respawn" option, or use script which automatically poweroff when application terminates. Read "man 5 init" for more info.