If I'm currently running XP and have a complete backup of my entire hard drive, and now I upgrade to a new computer running Vista, can I use my SP backup to install all of my old programs and files to the new computer without messing up the operating system?

No you can't do that because what ShadowProtect does is pull a 1:1 copy (content-wise) into a single handy file. It is agnostic with regard to your Windows installation with exception of the pagefile and hibernation file and some system startup stuff when doing HIR. It serves as the final (strong) straw when your computer data get damaged beyond repair or the whole computer gets stolen so you can rebuild the whole hard drive with an easy to use tool. It does not help you with migration. Usually you are better of just reinstalling all apps on the new computer. Migration of data can be hard because many vendors have not tried hard to make this easy for users.