Mazdaspeed Forums - 2012 Mazda 3 starts and dies, won't restart

Hello everyone, newbie to the forums here. I apologize if this is a repeat thread, I tried searching for the issues and did not see a comparable thread. Also this is a plain jane Mazda 3, not the speed package, but I thought there are enough similarities that maybe I could find an answer and help others as well.

My daughter has a 2012 Mazda 3 with about 55k miles on it. We have had zero trouble with the car thus far ... until yesterday. The car started as usual, then revved itself up and down for about 15 seconds, then died. Trying to restart it yielded a turn over and then nothing. It seems like it is flooded to me. I let it sit overnight, got the 15 seconds of running and revving the next morning then the flooded behavior again. Here's a video of the behavior. I want to reiterate I did not touch the gas pedal as the car revved up and down, that seems important to the problem: https://www.youtube.com/watch?v=X77J55tSTfY

I replaced the battery because after a few cranks the battery ran down. After charging it tested bad at Autozone.

She had not gotten gas in the last several days, but I drained the gas by jumping the relay (using these instructions, a GREAT tip!) down to about 1 gallon left and put 5 gallons of premium in it. I primed that in the same way, put everything back together, and got the same 15-sec run then flood result.

I have a new relay coming in tomorrow but thought I'd get on here and see if anyone has a suggestion. ANY suggestions would be greatly appreciated!