Group: Awaiting Activation
Merlin is correct but that doesn't mean you might not find some obscure piece of software on the web that says it will do it.
Acronis used to have (maybe still does but I ditched it a long time ago favoring Reflect robustness to flaky, obscure features) to backup applications. The catch was that it had to be an application that had the necessary information about it incorporated into the backup program. This allowed it to find the bits and pieces scattered over the disk and in the Registry. At the time the applications it would backup were only the very popular ones.
In your case, I think I would:
Ensure I had a current image
Clean all the unwanted stuff off the disk leaving just the OS, the application in question, Reflect and whatever else you deem essential.
Ensure the system is working as intended and if so, make a new image. This is now your base image for Windows and you can go back to this "new day 1" image at any time and still have your application available.
If you like playing around a lot and your application is not real complex whatever that means, you could:
Install a new version of your Windows (same version as on old disk) without anything else on a different disk.
Go to your old disk (the one with the application) and copy things like Program Files, Program Data (it will depend on the version of Windows and 32 or 64 bit version) how the folders are listed etc) and copy the files to the new disk.
Go into the Users Folder and look for anything that may be applicable to your application in all the sub-folders. Copy them.
Examine the Registry for any entries pertaining to your program. Copy them and insert into new registry using your favorite registry editor.
When this doesn't work, look for something you missed on the old disk such as it sticking a .dll file into .../system32 or elsewhere.
This list likely isn't exhaustive since I've never tried to do it but demonstrates the idea.