12 volt issues and disconnected vent tube

I have a 2010 Prius that has been having 12-volt issues since it got cold out.
It needed to be jumped about 3 weeks back, and then I noticed that sometimes it was fine, and sometimes the car had no "reaction" when I got into it or pressed the power button - none of the usual hum etc. In taking apart the trunk to get to the 12v it was jostled and then everything booted up as though there was no problem.

About an hour ago, I went out to start the car and it hummed when I got in, but when I pressed the power button it did the typical fade on the dash screen that indicates 12v issues. Except after that, the check engine light turned on and the ! triangle flashed on and off. I got into the 12 volt in the back and noticed two things - the vent tube was completely detached from the battery and there was wetness in the underneath cavities the battery sits over. I reattached the tube and tried to start the car again. The ! triangle went away, as did the check engine, but the car did not start. The power button started flashing green (???). The entire time I was working on the car it was making the hum that indicates it was ready to start up.

I think that there isn't enough oomph in the 12v to start it right now, but am wondering if
1. The temps are affecting the 12v (temps have dropped from 48F yesterday to 18F tonight and it is snowing)
2. If vent tube not being attached caused the issues I have been having with the 12v?
3. If the wet was rain/snow (we get a lot) is getting in or something more sinister, and could be part of the problem?

Car history: car was hit by a semi on the battery side, in 2019 - most of the damage was to the front and doors. Toyota did the repairs. Car has been driven pretty infrequently (once or twice a week most weeks) since the pandemic started, but since the jump start, have taken at least 8 20 minute interstate drives.

Any thoughts?