2003 Prius: left dome light on, 12v ran down, stalls out now.

I'm new to this site and am hoping that there are a few people out there that might be familiar with these issues.

I own a 2003 Toyota Prius. From what I understand, it has a significantly different design than later Prius models.

I went out of town for about a week and accidentally left a dome light on.

When I came home I tried to start it and nothing happened. No lights, no beeping, screen was dark, even the automatic locks wouldn't work. I deduced that the "starter" battery in the trunk had run down.

Next, I tried to jump start the 12v in the trunk. This gave the vehicle some charge after only a few minutes so we disconnected the cables. I was able to turn it on (inside lights and beeping came on) and get the combustion engine to start for a few seconds before it would stall out. Throughout this whole time the error message remained on the screen and beeped at me.

(I have gotten this message before. The engine would stall out (either while driving or in park) and the accelerator wouldn't do anything (pushing it actually seemed to slow the vehicle).
If I gave it some time on the side of the road or a few hours for it to "chill out" in my driveway, all of the issues would resolve themselves and I could drive away. Sometimes the error sign stayed up for a day or two after before disappearing.)

Thinking that it might be time for me to finally replace the 12v, I bought a new 12v battery that had the same dimensions as the original. Once this had been replaced I was able to use the radio, windows, automatic locks etc.

When I tried to start the car, however, I received the same error message and the vehicle stalled out again (after a few seconds of having the combustion engine engaged).

(It may be worth noting that after replacing the 12v, the combustion engine stayed on a little longer than with the original battery (the one I jumped earlier). Letting the car sit overnight with the new 12v led to a very small improvement in the amount of time it stayed on.)

Putting the car in "Ready Mode" resulted in the same stalling and subsequent loss of the "READY" display on the dash (from what I understand, I should be able to charge the main battery with the 12v while in "ready mode").

It may be worth noting that after replacing the 12v, the combustion engine stayed on a little longer than with the original battery (the one I jumped earlier). Letting the car sit overnight with the new 12v led to a very small improvement in the amount of time it stayed on.

At this point I think I need to tow the vehicle to a nearby dealership to have them take a look at it. I am a little skeptical, after reading some similar threads, about their ability to properly diagnose and correct this issue, however.

What do you think?

Did leaving the light on also discharge my "main battery"? If so, is there a way to charge/jump it myself?

Thanks for reading! I'm hoping that I can resolve this without going to a dealership and getting a tow as money is tight right now.

- sadwithoutmycar