Usually everything(really just most things) goes dark, emergency lights come on. You are on battery power with it slowly depleting. PA probably still works so you could say a few calming words to the pax if you have pax on board. With these major airline opeations, it seems that most pilots don't get to see what it is like when just on battery power. Depending on type and systems, expect a delay if this happens just before pushback. I had someone screw up a switchover from ground power to aircraft power recently and it resulted in several strange false warnings that took more than half an hour for maintenance to solve. Had to do a complete power shutdown with all the test warnings during power up to fix it.
As for the ADIRS switch, that would be specific to the 777(maybe some others as well) with the ADIRU switch.