John - Sticking with drive G:
You might not be doing anything wrong.
You say that you can see it and its folders and files from (My) Computer on your laptop.
Can you manually navigate to the folder where your correspondence is kept on drive G:?
If so what are its properties - from the right click menu?
Can you copy the whole folder and paste it to drive C: on the laptop?
If so what is now in it?