From where you are there are the presence of the wifi radar logo on the iPad it looks like you are at least logged in to wifi on the AE. Quit that screen and open Airport Utility and try to setup bridge mode from there.
That last message look like the AE is not detecting any IP at all.
Do you have another device with wired ethernet you can verify that ethernet port in the room even works? I'm starting to question if it does. You should be able to take a default settings Airport Express, plug it in to that ethernet cable and get a green light even if you can't login or get on the Internet, the AE should still get a green light from just getting an IP address.
That last message look like the AE is not detecting any IP at all.
Do you have another device with wired ethernet you can verify that ethernet port in the room even works? I'm starting to question if it does. You should be able to take a default settings Airport Express, plug it in to that ethernet cable and get a green light even if you can't login or get on the Internet, the AE should still get a green light from just getting an IP address.