With a truly DEAD CMOS battery, it should be Impossible for any PC to boot up, even to the BIOS.
But that's only from 40+ years of experience, as a working PC Tech, so what do I know?
I
think this might have changed, though at what point I'm not sure. I do know that both my previous rig and my current rig will attempt to boot, and POST will put up dire sounding warnings about the CMOS battery to being there, and all info is default, yadda yadda, yadda, but I can usually enter Setup, adjust some settings, save and boot.
I might try exactly that with my desktop as it;s battery has to be over 4 years old, now, with the manufacture date of my mobo, so it might be a good idea to pro-actively replace it - and, naturally, since I am replacing it, it would be a god way to test my memory. I can see if it will, in fact, boot without any presence of a CMOS battery at all.
And, technically, is
should - the battery is there to provide active power to store the settings (including the clock as a setting) in the CMOS / EEPROM, nothing more. It should not prevent the BIOS / UEFI from actually booting, or at the very least,
attempting to boot. That would not make a lot of sense.
But, HP is ... HP. Lol. So I would not be surprised if they engineered their mobos / BIOS that way.
Could it have been a business-focused device, so as to prevent data theft from a device that had been locked down with a boot password?