If you have copied the contents of the old C Drive your files will be there, it is just a matter of finding them.
Go to the location of the copied files and look for a folder called 'USERS' it is normally in the root of the C Drive (original HDD).
Once you have found the 'Users' directory open it up and you should see a folder with the same name as your old laptop logon name, open that folder and you should see a folder called 'DESKTOP' it will more than likely have a different icon to the beige ones you see most of.
Open the 'Desktop' folder and your desktop folders and files will be showing.