Had a similar one on my Pocket. Ended up have to send it to Berlin for repairs. Not only had it sat long enough for the batteries to go flat, one of the 3D printed battery supports had broken, and the pieces rattling around inside the case broke a few thermistors on the charging board.
In your support ticket, you may want to request a new backplate if it has to go in for repairs. A lot easier to do both at once than to charge you tariffs on two shipments.
If bypassing the charger doesn’t work for you, then you could try buying some extra jumpers and going through the process of reflashing the system controller, since you’ll need one jumper to bypass the charger and move the two existing jumpers to power the board. That should at least get you to a workable system without being battery-backed. (See support.mnt.re and follow the “unusable after firmware update” steps for how, but with the charger already bypassed and the board powered from the usual USB-C port).
If you’d like, you could also get some new LiPo batteries (see elsewhere in the forums for details). Obligatory mention that if you do, be mindful of the polarity and swap the connector around if necessary. I bought these but they were the wrong polarity, and used some tweezers to do the swap. There are some guides online on how to do this.
Did some additional looking inside the bottom section mostly out of morbid curiosity, and found the remains of TH2, the thermal sensor on the right side of the charger board. So that explains why the charger doesn’t work.