You'll be up and running shortly, this place is full of knowledge.
I personally haven't used the "AnyDVD Ripper" aka. "Rip Video DVD to hard disk,,," (right mouse click on the fox in your menu tray) feature within AnyDVD but some say its the bomb for troublesome DVDs.
None-the-less this wouldn't solve the "can't copy any disc now" problem. Can you post the error message your getting?
What happens when you use the "Clone DVD" prompt? Setting up the source as being straight from the disc drive opposed to copying it to your hard drive then to disc? Basically just making a straight disc to disc copy, eliminating the hard drive as a factor.