The old HDD may or may not boot in the new system, it depends on how different the motherboard chipsets are. If you get a successful boot into windows, you can install the new chipset drivers, and use Device Manager to uninstall the ones not needed on the new system.
Long story short, you need to buy another copy of Windows. You will be violating the End User Licence Agreement of Microsoft. You are buying a new PC, even if you build it yourself. Too many changes to the previous OS's hardware...but...
The best way to install the OS to your new build is to do a fresh install, formatting the drive during OS install.
Clean install. Use a program like clonezilla, free, or Home Partition Wizard also free and has a GUI to clone your drive. After fresh install of seven move over your user files and other files like save game files and stuff. Imaging is going to just reload all the old drivers because it was imaged from the old hardware same with cloning as i described above. You don't have to buy a new copy of 7 if you are going to only using it on one PC just reactivate and when it asks for how many installs have you done you say one. BAM its registered done this at least 3 times myself. Had to call microsoft one time because I said no installs since its the same computer just with new hardware. Sorry my reply is so long.