Well, I figured it out on my own I think.
Apparently the problem has to do with some sort of a permissions problem.
All I want to do is use the WD external drive like a big USB flash drive .. plug it in and copy files to it .. but, alas, it has some security "feature" which assigns permissions and ownership to the drive and folders you copy to it.
So, here's what has to be done as a workaround:
on the computer which shows the "access is denied" message, follow the directions on this page:
This link shows "How to take ownership of a file or a folder in Windows XP"
you basically do the following steps:
1) Disable Simple File Sharing (Start --> My Computer --> Tools --> Folder Options --> Vew tab --> Advanced Settings --> uncheck "Use simple file sharing" --> click OK
2) My Computer --> right click on the drive (e.g. F: ) --> Properties --> Security tab --> click OK if security message appears --> Advanced --> Owner tab --> in the Name list, click user name or Administrator --> select "Replace owner or subcontainers and objects" check box --> click OK --> click Yes --> click OK
If this is not right, please let me know.
If this is right, I hope it helps someone else with the same problem