Please do not suggest the '4 second press, 5 minutes without power' solution as it has already failed.
I have already tried the battery reset button and it did not work. However, it seems that the actual BIOS ROM image does not survive extraction and is unavailable when I run the InsydeFlash.exe utility from the extracted ZHK116 contents. I have extracted the ZHK116.exe file using 7-Zip and edited the Platform.ini in the archive to disable the battery check. This introduces a 'chicken and egg' scenario where the problem I'm trying to resolve with a BIOS update is directly obstructing the BIOS update. However, the InsydeFlash utility obtained from Acer's 'Support & Downloads' page will not run the BIOS update until the battery is at least 15% charged.
As a part of my efforts to remedy the problem, I am trying to flash the BIOS to 1.16. I have an Aspire ES1-111M-C7DE whose battery is failing to charge.