Flashing the BIOS is certainly something to be done very carefully and I've
done it only when absolutely necessary, maybe 5 times, almost always by
floppy. It only failed once, due to a defective mainboard, which was
cheerfully replaced under warranty. Never had to do it from a boot CD but
the principle is the same.
Have you ruled out the possibility of a boot sector virus? If I had a
machine that wouldn't install that's one place I'd suspect. . .