There is a possibility that AnyDVD has picked up an incorrect driver letter which is not pointing to your DVD/RW this can happen.
I have had a similar problem happening to a friend as well. What you need to do is to go to the system manage in Win XP. This can happen if you have any other buring software that installs virtual CD/DVD ROms in the system.
Right Click on My computer Icon on your desktop and then select manage. Now click on the Disk Management and you will see all the drives including the Optical devices in your system.
Now compare the drive letter that the AnyDVD has picked up as a letter to your dvd rw drive and you will see what the problem is.
You can try to re-assign ( change) the drive letter of your DVD/RW to the letter that AnyDVD has picked or visversa. That should solve your problem.
Give it a shot and if it does not help write back with a bit more info specially what drive letter is associated to your AnyDVD as I susupect as Olli had said some how the program has not been installed correctly.