Timestamps of manually changing cells

Hi everyone. My first post here. Found this forum by accident and can't believe I've been doing it "the hard way" all this time. Excellent forum!

What I ultimately need is a timestamp for each time a user changes a particular cell (and I'm trying desperately to avoid macros). I've read this thread http://www.mcgimpsey.com/excel/timestamp.html which does almost what I need.... it timestamps when a user changes a cell from blank to nonblank (circular references on purpose? bloody genius! ). What I need is a new timestamp each time the user types over the old value and enters a new value. I cannot trust the users to delete the cell(s) first, or even to simply push a button for a macro at the approprate time. And if this calculation is off the whole rest of the program falls apart.

Anyway, can this even be done?