That's OK; to go one step further since you've got it in your good computer (booted up to Windows right?) then you can do this to check and see if it's all there, byte for byte:
Open two My Computer/Windows Explorer windows up and in one, go to the i386 folder on the broken computer's hard drive, then in the other, go to i386 on the setup CD.
Without selecting any files, right click on a blank area (might need to scroll to the end of the list to find a blank area big enough to hit) and select Properties. Do this for both of them. This will do a properties check on all of the files in the i386 folders. The CD will probably take longer to do than the hard drive. Move these property windows around so you can see them side by side
Once they are finished updating, then you can see the full count of all files and folders and exactly how much space it takes up. You will probably see two figures, one being "Size on disk:", which will likely be different than the other anyway. You want to compare the one above it that says "Size:", and the one that says "Contains:"
edit: oops. Looks like you already did that.
Alright, so now it sounds to me like it could be the hard drive going wonky.
Right click on the disk drive from my computer, then go to Properties. In Tools, start an error check. Don't check both checkboxes unless you want the scan to take a very long time; the scan for bad sectors (bottom checkbox) will literally scan every piece of the hard drive and see if it's suitable for writing/reading data.
However, if it does not find any errors in the initial scan then I think I'm out of ideas at the moment for why it could be failing to copy files.