There's a problem with your video link. Nevermind, it didn't load right the first time for some reason.
I think you should make damn sure that new battery is fully charged. It was sitting on a shelf for a long time at a store, and it didn't really charge in the time you had the car running. I know it has 12.4 volts, and that should easily start a car if all the batteries cells are there (and they should be with a new batter), but you never know.