Car won't go into reverse (automatic transmission)

So I get in the car today to take it in to the transmission shop, but the engine won’t turn over - just keeps clicking. The red low battery light is tittering, like a light bulb with a bad connection. After I jump the car, I notice the battery indicator is already at 14 volts, and I’m like, whoa that’s odd. But every indicator light is going bonkers - emergency brake (though it’s released already), ABS, service engine, etc., just turning on for a bit, then going out, then back on, and I’m like, whoa, that’s even more odd.

I drive it around the corner to let the engine idle a bit longer in a legal parking space, and when I shift the car into park, the engine just dies.

Does this tend to happen when the sun shell is broken, is something else wrong now, or does my car just hate me?