+1 for what Acejam said. let it sit for a minute before trying to crank. If it's not going to do so (like what we saw in the video) don't just keep trying to crank it. It looks like your ECU is initializing the start-up sequence over and over again. While probably not exactly bad for the car, can't be helping anything.
If letting it sit for a few seconds before trying doesn't work, turn it off and start pulling some voltages. Forget about what the AP is reading, see what a multimeter is reading across the battery terminals. If you're at 11 or less, your battery is probably toast. If you jump it and do get it going, then see what the AP says. It could be you have a bad alternator as well that's not charging the battery. Really easy fix and a relatively cheap part.
Also, double check to make sure that the flash was completed on the AP. Back when the AP first came out, there were a billion and one threads about people's cars being dead because they didn't let the flash complete all the way. Make sure you did so.
Let us know what the multimeter reads out. If you don't have one, invest in even a cheapo one from Radio Shack.