Hook the system drive up to the new computer so that it is in the system drive position. If there are other drives, hook them up so that they have the same drive letter as on the old computer. Start the computer. If it works, it works and you just saved yourself a lot of work. As I said, I have done this successfully before.
If it does not work, turn off the computer and move to plan B which is installing Windows on one of the new drives and hooking the old drives up as additional drives and reinstalling all of your programs. Unless your drives all have the same drive letter as the old computer and the programs are in the same place as they were on the old computer, an ALL.REG file will do you no good.