WD 1 TB External Hard Drive Problem

I bought my WD 1 TB External a couple months back.  I do not actually own a computer, but I do have access to computers that I can sign out for long periods of time via work, so I got this to back up all my files before I have to return the laptops.  I had no problems clicking and dragging on my old PC laptop, that ran Windows Vista.  I was even able to use those files when I connected my WD External to a Mac laptop that I signed out for the summer.  But, now that I have to turn this laptop in, I’m having problem connecting to it at all.  I never set a password, and never tried to lock it, but when I open the My Book drive, and try to click and drag, I’m getting an error message that reads "The item cannot be moved because My Book cannot be modified. 

How do I back up my files?  I have so much on this hard drive, now, that it’s slowing down the performance of the laptop, and I need to hand it in within the next couple weeks.