OK, guessing here, but....
Intel APIC Architecture is a system of Advanced Programmable Interrupt Controllers, which are used in SMP systems. NT obviously sees your machine as having 2 cores (which is an SMP system) and is trying to load a suitable IO APIC.... and can't because it can't find a suitable one. Result? Non bootable.
Now, again I am just guessing here, but the HAL.dll being loaded is simply out of date. So, I don't think a BIOS update will help, its the software that's too old not the BIOS.
Instead, can you try to get an installation CD of NT that already has the latest service pack (6a, I think) slip-streamed in? Whilst I've done some research on this and believe that its impossible to make such a CD (as you can with 2000/XP/Vista, etc.) but you might be able to get hold of one with SP6a integrated from Microsoft themselves. If you hold a valid NT4 licence, they might actually supply you with the CD free of charge or for a small handling fee, but there's no way to make the CD yourself with NT4 as far as I know.
Also, is it possible for you to disable one of the cores in the BIOS? (I don't have a dual system so I don't know if that's possible, but it might be) That might let you install NT4, then install service pack 6a, then turn the core back on. Just a thought.
