Hi:
That is very odd that the control-A method doesn't work.
I have attached the old electronic serial number programming tool that works on many HP business desktops.
I know it worked on models up to and including the 8100 Elite CMT (made around 2010), however I have no idea if it will work on the Z840.
You will need to use a USB FDD, and probably you will have to run the utility on a XP computer for it for format the floppy disk and make it bootable.
It cannot be run by any other means.
Other than that, you would have to take it to an authorized HP service center and have them tattoo the BIOS with the serial number on the case sticker.