Winter is coming, and I think my battery is dead/dieing

ThreeSeven

https://vid.me/GGbH

This was happening to me a lot last year although usually the car would start up after a turn or two, it's an AT. But this morning when leaving for work it just kept doing this. Did some Googling, saw a recommendation to unplug the negative terminal on the battery for 10-15 minutes but that didn't do anything. Other recommendations included that the battery on the key fob might be bad, so I replaced it and even tried the second key fob but that didn't help either.

When this happens the brake pedal stiffens to the point of basically being locked up. This really only happens when the weather starts getting cold here in California. Temps around 55 degrees at night right now. I drive it a couple miles to and from work every day, not usually out on long trips.

I don't have a voltmeter so I was going to take the battery down to Autozone and have them test it. I'm hoping it's the battery, it's an '09 with 42k miles on it, 10k of which I have put on it as I bought it used 2 years ago.

Just wanted to post and see if anyone could help me out before I head out.