No, each activation 'hash' is generated by the computer on which the software is installed. As for being counterfeit.....that's certainly a possibility. The problem is that a retailer will almost certainly refuse to refund your money once the software package seal has been broken, unless you can demonstrate that the software is faulty - and that will be difficult.
Have you contacted Microsoft about this? I suggest that you do - they'll soon tell you if you have a counterfeit copy. Does the CD have an authentic-looking Microsoft hologram, and is there any documentation in the box?