The light only flashes when I close the battery door for the first time. It does not flash again when I open the battery door without taking the battery out.
This doesn't answer the question

In normal circumstances it should blink every time you
close the battery door.
You wrote that it will blink when closed and won't when you open... but what if you close it again?
The battery is fully charged and I do not have a spare battery/wall adapter.
It is still possible, but unlikely that battery is dead. I had LP-E6 reporting fully charged that was really dead-dead in the past.
If you have any friend with another camera that runs LP-E6 / LP-E6N, borrow one and try. This is the most common Canon battery right now.
I cannot fully remember. I believe the camera lost power first without any me opening the battery/battery door. I did end up both opening the battery door and removing the battery.
I remember formatting the card in the camera, then turning the switch off then on. It is likely that the camera did not turn on when I flicked the switch back on so I removed the battery.
All the symptoms so far points to potential hardware failure. Your description and camera behavior ( + fact that roms run in QEMU) suggests that this may be power switch related, and it started misbehaving when it powered off on you.
Power switch problems are quite common theme in this subforum, and they can produce any number of unusual symptoms.
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If you are tech-savvy or have a friend that doesn't fear tinkering with hardware - try disassembling the camera and verify using multimeter if power switch works fine. It would be also good to connect to debug port (UART) and grab logs from both channels to see what camera wants to tell us.
Debug port should be located in bottom right corner, there's a hole under a thumb rubber (white 6 pin connector with nothing connected to it). Pinout should be easy to check with multimeter and USB UART adapter.
Thread on debug portUnfortunately with no real logs saved from camera I have no idea how to go any further.