What version of VISTA -- OEM or Retail ? If it is a Retail license then yes it is transferable to the new system -- If it is OEM it is a bit more fuzzy -- In an OEM license the activation is tied to the original MOBO and is only transferable to a new MOBO if the old MOBO is damaged and replaced with a comparable MOBO (ie. If available same Make\model from the same OEM - if not available in same make\model then a comparable warranty replacement board from the OEM) - The reason for this is that the OEM is responsible for providing support on that license and they can not be expected to provide support if you no longer use a system they built so allowing users to move the license to a new system would not be fair to the OEM left providing support and MS does not provide support for OEM OSes so you would then have end users left with systems that are using OSes that noone supports.

That said in your case since the old MOBO has died and that is the cause of you changing it they may reactivate the license ( it might auto activate depending on how often you have already reinstalled things or you may have to talk to a MS rep (at the activation line that the number will be shown to you if it fails to auto activate) and explain that your old MOBO died requiring replacement in which case they normally will provide a new activation code to you.

However to get that far you are going to need either the restore disk from the original system or the windows Vista installation disk ( since changing the MOBO is going to need a REPAIR installation done since it will be on a different chipset and require different drivers) -- so hopefully you have those (either came with the system or are installled on a hidden partition so you can create a restore disk after purchase deppending on the OEM) --- After installing the HDD on the new system on first boot you will want to boot from either the recovery partition or the DVD\CD and run a Repair Installation as most likely it will not properly boot from the HDD due to different components needing different drivers installed to the HDD. (and truthfully to avoid problems later it is usually best to do a full reformat\reinstall of the OS instead just to be sure there are no lingering issues brought forward to the new system (so making a backup of important files and then reformatting the HDD and reinstalling the OS from scratch is probably best !)