I was having the same problem, but I figured it out with enough experimenting.
First, read over this link: http://lovelace.augustana.edu/q2a/index.php/481/how-do-i-access-my-h-drive-or-the-s-drive-on-my-own-laptop
What worked for me was to map the H: drive BEFORE trying to log in to the server. When you try to map the drive, it will ask you for your credentials. Follow the instructions on the article above and it should work.
I tried going the other way at first, and I kept getting the "Access Denied" message. Sounds like this is happening to you as well. Of course, this was all done with a Windows computer -- if you have a Mac or something different, you should contact your professor for further assistance. As far as I know, there aren't any articles on here for accessing H: or S: drive on anything other than Windows...
Hope this helps!