Okay. Sounds like a stretch, but I'll give it a shot.
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Also, I have some arm9loaderhax.bin.bak file on the root of my SD card. Is that normal?
Edit: reinstalling the cia files didn't give me an error. They are reinstalling. Will report back once they have finished to see if the saves were saved.
Having a Arm9LoaderHax.bin.bak is not normal unless you used some kind of program to manipulate it, which creates backups automatically (like certain hex editors).
I don't think the payload is the problem, because if so the 3DS would turn off immediately.
The only reason I can think of for this to appear is a faulty NAND.
I am assuming you are using a SysNAND setup and it was indeed working before, from what you wrote. (Correct me if I am wrong)
Please check if your Luma3DS (which I think you are using?) is set up correctly and make sure your config is set correctly and you have "SysNAND is updated" checked.
Are you using a non-screeninit or a screeninit version of A9LH?
Edit:
As your older NAND Backup seems to work don't mind this.
Saves are stored NAND specific on the SD Card. So as long as you didn't format anytime in between and acquired a different NAND ID your savefiles will still be read as before, as long as you use the "newer" files from the Nintendo 3DS folder on the SD Card.
As stated before the games etc are also installed on the SD but are not visible in your Homemeni because they are missing in the titledb.
You can still launch directly from DevMenu.
To get them back into the titledb you can simply reinstall the games via FBI. (Or acquire the "newer" titledb from the "newer" [bricked] NAND if you backed it up.)