I actually misread your first post. I thought you were planning on just putting it in and booting from it.
But in the scheme of things here, what I said still is valid. If you do not boot from the drive you are taking from the old computer, you will not be able to run programs from it. Windows needs to have that information in the registry, if you aren't booting from it then Windows will just expect the registry information to be in the registry of the install you are running.
I don't think you can just copy the registry over. You might be able to boot the old install and extract specific parts of the registry and then load those in the new install, but I think it would be a time consuming and tedious process, and one likely to introduce further problems.
So, my advice, since you are getting another drive and another Windows install. Would be to try and boot off your old drive and just see if it works, I have heard of this working particularly well in Windows 7 compared to say XP. I would try to boot into safe mode originally, then go in and uninstall all (or nearly so) of your hardware from Device Manager. Then reboot and hope Windows detects it all again (otherwise you just have to go out and manually find/install drivers).