[mothered]

I've had 4 HP lappies die on me, hence as of many years ago, I'm done with HPs.

I'll try and simply this as best I can.
The primary function of the CMOS battery, Is to make sure the BIOS settings are Intact and to store the correct date and time, hence your above post of "dead RTC battery"- RTC being "Real Time Clock".

If the CMOS battery Is dead/dying, the BIOS will most likely not get the correct Information from the CMOS (thereby cannot Identify the date & time settings, hardware configurations etc), thus consistent with the unexpected shutdown you've described.

As mentioned, change the CMOS battery and reply with the result.