What is your computer doing during that minute or so while HZ is unresponsive? I know, that's a big question. Let me narrow it down some:
Is the hard disk grinding away, is it silent, or is it clicking?
Does the mouse pointer respond instantly, does it lag behind, or is it non-responsive to movement?
What happens if you hit ctrl-alt-del? Do you get the task manager or lock workstation menu instantly?