HP desktop asks for a power-on password nobody set

Read the exact wording on the prompt first. If it says hard drive / HDD password rather than power-on, that lock is stored on the drive itself, so the jumper or CMOS battery won't touch it. Different problem entirely. And if you bought it second hand from a business seller, ask them. They often have the password on record and it's quicker than any of this.

That's a BIOS password, and someone did set it at some point, could be a previous owner or an office IT person if it's ex-business. Don't keep guessing. After 3 wrong tries a lot of HP machines show 'System Disabled' with a code, which is more hassle. On HP business desktops (EliteDesk, ProDesk etc) there's usually a jumper on the motherboard labelled PSWD. Unplug the PC, pull that jumper, boot once, password cleared, then put it back. Pulling the CMOS battery often does NOT work on those because the password is kept in separate memory. On cheaper consumer models clearing CMOS sometimes does it. If neither works, HP support is the route, with proof of ownership.