Where you put FS at makes no difference at all Internal or External as long as your short cut points to the right place.
Any time you install any program your system will make Registry entries so your system will know where to find it at.
What can happen if you have moved FS than your system does not know where it is at. Usually all you have to do is to just edit the shortcut and point it to where FS is now located. The other way would be to reinstall it. But with out Disks this is a lot harder to do.
What I do when I want to back up a program that is on disks is to format some disks making sure that there is nothing on them than copy one disk to another. In the case of FS2004 the original disks are CD'S I use DVD'S so it will not take as many I think it only used ONE disk.
What operating system did you use to make the copy that you are using.
This could be a issue but not 100% sure I could be way of base
Older versions of Windows used a file system called FAT32
Newer versions use NTFS
There are some differences between the two but do not want to confuse you. Most of the issue has to do with copying one type to another things do not get put in the correct place and you can loose some data.
Like I said I could be way off base here
But there are some issues when converting form one file to another that might cause your problem,
Below is a link that would better explain this.
https://www.google.com/search?q=can+you ... ile+system 
