If you know your serial number, then I would suggest that you try to use it on the new PC, I am not aware of any way to deactivate a dead installation! If it does not work then you will have to contact BI support, I presume that you have an active support contract, if not then hopefully you have a backup copy of the full installation package from some time during the period of time when your support was still active.
Just out of curiosity what failed on your PC, was it the HD or the motherboard?