Ok, problem fixed. I'll try to explain what happened and how the problem was fixed.
You can read what we did upto the point when we were constantly getting the "Reboot..." message.
It turns out, that the EFI boat loader had been damaged during the night when there was a power cut (we are in the Caribbean). The first time I turned the machine on in the morning, the system still had the boot loader from the Debian installation to boot up to. However after the power supply failed completely (it had to be replaced), and the boot loader file was destroyed.
The solution was to get a boot loader from a functioning linux machine, edit the file, copy it on to the USB stick in the Rescue install directory, boot from the stick, and then at the appropriate point of the installation we chose Rescue installation, then went into the command line. The boot loader was then copied on to the first HDD, renamed so that the BIOS would read it as it's own. We then restarted the machine, and when it came up without a problem, we did the same thing to the second HDD.
When we restarted the machine, the linux guru ran through all his checks and explained exactly what had happened, and what he had done. At the time I wasn't too attentive, I was just happy that the @#$@# was up and running. He did say that the clue for him was that the mother was a UEFI motherboard. I have to admit that since I haven't done too much of HW building in the last 4 or 5 years, so UEFI/EFI didn't mean much to me.
SO, I'm just glad I have a linux guru working with me, and we managed to get this up and running.