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The answer is YES, you CAN transfer your Product key from ONE computer to ANOTHER.
However, you can ONLY use the product key for ONE computer at a time......so you MAY have to call microsoft to let them know, that you are doing this. As they take records of what computer was assigned THAT SPECIFIC product key. Now, sometimes it will auto update, and sometimes it wont, and in the case that it wont....when you try to enter the product key for Office 2010 on your new computer....it just wont work, and you will have to call microsoft to clear up the assignment.