|Would I have better luck just copying it onto the laptop?|
Yes, that is the correct way t do it. No need to open a file in order to copy it from one place to another.
However if you are getting Access denied you may need to take ownership of the files. Although you own the files, they would have been created under a different user account on the desk top than the laptop.
This will tell you how:
If these are MS word documents just make sure you have MS Word installed on the laptop in order to read them.