@ChrisRowland , I faced this a couple of times. For me, it appeared to be a corrupted BIOS and may be related to nvram getting munged.
Try this. In one case it did work for me.
Create a bootable cdrom or USB 2.0 thumb drive (8GB or less, I used a 512mb drive!)
Be sure to name it HP_TOOLS
On it place ONLY the BIOS BIN file that WAS working.
Put the CD or USB drive in. Make sure the USB is in a 2.0 port, of using that media.
Power up. Wait. Wait. Wait. Be patient. Wait. It may take 3 minutes or 30!
Reboot. Be sure to enter into BIOS settings immediately and check and attempt to save your changes if you are able.
Be sure to remove the CD or USB immediately after first successful boot and so that you don’t begin anew the BIOS recovery method.
The HP Compaq 8300 Elite series are supposed to be able to do a BIOS recovery using this method.