Do you have your original hard drive? If so you can boot from it and capture your original W7ProCOA..... there are little utilities that let you do that, and it is legal to know your COA codes.
If it was from HP have your captured your "Restore" media from that drive? Best is onto a thumb drive, 8GB size is perfect, with lots of room to spare. If you use Restore media it will give you the single HP OEM COA code. That code cannot be used with a clean install from a W7Pro64 system builder DVD, however.
Ultimate..... I have had some very bad experiences with that versus W7Pro64. However, it may be due to an issue with Windows Update. Find my post on that issue.... critical..... and the solution has to do with starting the install with zero internet connection, adding two MS updates, and thereafter hooking up to the internet for proper update experience. There is a very bad bug in Windows Update that to my knowledge has not been fixed yet, but this is the way around it.
Search that out before you begin.