Cannot boot without wall-power, green power LED on plug-in

After an indeterminate time unplugged from wall power, the laptop fails to boot. Upon plugging it back in to power, the power LED stays solid green for a good while.
This does not appear to be an issue with the main battery, as it still appears fully/mostly fully charged right upon boot, and the laptop can be used unplugged for a while before it abruptly stops working.

Things I have already tried:

Things I haven’t tried yet but plan to (unless anyone has any better ideas)

  • Replacing the CMOS cell

  • Which OS (Operating System)?
    Linux (not expected to be the problem)
  • Which release of your OS (Operating System / Windows 10, 11)? (if you are having a Linux related issue, please create your thread under the Linux subcategory)
    Arch Linux
  • Which Framework laptop (11th, 12th or 13th generation Framework laptop, Chromebook or Framework Laptop 16) are you asking for support with?
    11th Generation Intel