2006 Prius no power

Hello all! First time poster here hoping that you can help me out of a bit of a pickle.

I have a 2006 Prius with 91k miles on it. I drive it to work (50 miles round trip) every day, and often across the state (500 miles round trip) on the weekends. This evening, I came back from one of these cross-state trips. The car drove perfectly with no issues, until I pulled it into the car port and turned it off. As soon as I hit the power button, all of the lights on the dash, the speedometer backlight, the lights on the front panel buttons, along with the interior lights began flashing on and off randomly; it was like the car was having some kind of spasm, turning on and off every light in the car at random. The external lights were flickering as well. After about 30 seconds, it stopped and the car went dead. It would not respond to anything.

I broke out the voltmeter and tested the 12V battery in the back. When going into the back of the car, I noticed that it had suddenly developed a smell like an open sewer; it is a very pungent acidy or rotting smell. The battery tested dead, pulsing between 2.8V and 3.1V in a regular pattern. I hooked the battery up to a trickle charger that I have, at which point the right rear brake light and license plate light came on weakly and started pulsing brighter in the same pattern that I had seen on the battery charge before.

It's now been charging for about two hours; the rear lights have stopped pulsing, but the check engine light is pulsing on and off inside with the same pattern again, and still nothing electronic responds (door locks, etc). The raw sewage smell is nauseatingly strong in there.

TL;DR - 2006 Prius running fine, freaked out electronically when turned off, refuses to turn back on and smells like raw sewage.

What is happening to my poor Prius?