Maxwell Edison, i’d like to add to the answers to your question…
As i understand it, you would like to know whether, when the hdd of the comp. is changed, just copying the files to the new hdd are enough for the comp. to be up an running as it were…
I would suggest that you first format the new hdd, assuming you need nothing from it, and then copy the entire backed up cd to the new hdd. The system files, registry files and all will automatically be copied to the new hdd ( this is assuming that you included every file in the initial cd backup - system files, hidden files, etc. )
In the case where the rest of the hardware of the computer remains unchanged, the computer should be up and running as if nothing ever happened ( other than showing up the new hdd in explorer with all new space and all ). You might want to make sure at this stage that all system files that originally did not have read only attributes are not now reset to read only. If they are, as Seven suspects they might be, simply reset them using the dos attrib command.
But, in the case that you wanted your old settings to work on a new computer ( which might have significantly different hardware components, such as display card, sound card, etc. ) this will probably cause some driver conflicts on initial boot up, which can moderately easily be fixed with a few more driver installations and 50 or so reboots 
Note that in the above mentioned cases, where the new hdd was formatted before the backup was copied, and then the backup was copied onto the newly formatted new hdd (
), all dll’s, registry settings, etc. will accompany the file copying… * i love the form that some sentences take when you try to explain some concepts on the board*
In the case where you overwrite the contents of the new hdd ( without initially formatting it ) you will still get a working hdd, but with significantly more conflicts to resolve. I suggest you stick to overwriting only if the OS versions of the two hdd’s were the same ( e.g. Win 98se with Win98se ) and you are sufficiently adept at resolving conflicts in windows.
I believe that there is software out there that makes this process simple, such as Ghost Image. I haven’t used any such software nor do i know their exact functions, since i always prefer working with DOS and doing a format and load, but you might want to further your research.
If you would like me to clarify or further expand on any specific points, do let me know. If you would like me to clarify my entire post, i’ll be out of town. 