I purchase a NEW Airport Extreme
What model number of AirPort Extreme is this? This is extremely important, otherwise we are playing a guessing game.
I plug it in
Plug the AirPort Extreme into what? A modem? Another router? We need the make and model number of the device to which the AirPort will connect.
according to directions, and the flashing orange light comes on
This is normal and expected.
but never goes to green
It will never display a green light until you use AirPort Utility to configure the AirPort Extreme with the correct settings. Even if the settings are correct, the AirPort will need firmware updates.
This is the same condition as the previous one. I have attempted to access it but it never comes up to be selected though a network shows it DIMMED so inaccessable.
Then, you did not configure the AirPort correctly. Will you be using a Mac to set up the AirPort Extreme? What operating system is the Mac using?