My father's 4000D had a problem not identical, but similar, to this. It wasn't crash-happy, but it did have the 1-second freeze symptom. Turned out the problem was caused by a flaky Microsoft PS/2 mouse running through an Amiga->PS/2 interface. Swapped it for a different mouse (a different PS/2) and all was well.
VERY strange. Might be worth trying if your other solution doesn't help.
