I got it to work finally, I didn't need to contact support!
For future people who have this problem, here's my info:
First, I uninstalled
all Slysoft applications -
AnyDVD,
CloneDVD, CloneDVD Mobile, and
CloneCD.
I use Ashampoo Uninstaller to take a system snapshot
before then
after a program install. This logs
all file changes, additions, and registry changes and additions.
I used each program's uninstaller from Control Panel -> Add/Remove Programs. After each uninstaller, I then loaded each log file into Ashampoo Uninstaller and deleted any file and registry changes the uninstallers didn't get.
Finally, I insured
all of these files and registry keys were no longer on the system:
C:\%systemroot%\system32\ElbyCDIO.dll
C:\%systemroot%\system32\drivers\AnyDVD.sys
C:\%systemroot%\system32\drivers\ElbyCDIO.sys
C:\%systemroot%\system32\drivers\ElbyDelay.sys
C:\%systemroot%\system32\drivers\RegKill.sys
HKEY_LOCAL_MACHINE\SOFTWARE\Elaborate Bytes
HKEY_LOCAL_MACHINE\SOFTWARE\SlySoft
HKEY_CURRENT_USER\Software\Elaborate Bytes
HKEY_CURRENT_USER\Software\SlySoft
HKEY_LOCAL_MACHINE\SYSTEM\ControlSet001\Control\Class\{4D36E965-E325-11CE-BFC1-08002BE10318}\LowerFilters
HKEY_LOCAL_MACHINE\SYSTEM\ControlSet002\Control\Class\{4D36E965-E325-11CE-BFC1-08002BE10318}\LowerFilters
(They weren't; Ashampoo Uninstaller got them all.)
After doing a final reboot for good measure, I then installed all four SlySoft products in the order that they were released, oldest to newest:
1 - CloneCD
2 - CloneDVD
3 - CloneDVD Mobile
4 - AnyDVD
After rebooting, everything now worked normal!
Some speculation:
When I installed AnyDVD 6.0.9.2, as with all previous installs, I got "Trial period expired" before entering my key. But when I was troubleshooting last night and did a reinstall when my net access was down for around an hour, I got the full 21 day trial. This leads me to believe that when you run AnyDVD setup, there is some communication with a server at Slysoft, perhaps it creates a hardware based hash and stores it on the server, and that's how it can track trials and expirations. I'm totally guessing on that though. I was able to successfully uninstall 6.0.9.2 and install the new 6.0.9.5 today. My net connection was up, and I did get the full 21 day trial again before importing my key.
The other thing some people have pointed out is that they can get the "No DVD Drive detected" error if they are running a
firewall like Zone Alarm. That
may be due to AnyDVD not being able to "phone home," or it may be a driver conflict. Again I'm guessing.
I believe my problem may have been due to an incorrect version of one or more driver files on my system, maybe ElbyCDIO. AnyDVD will update elbycdio.dll from 6.0.3.1 to 6.0.5.1, and it will also update elbycdio.sys. Both the old and new elbycdio.sys have the same version number (6.0.0.0), but the updated file is 15,440 bytes and the old one (from CloneCD I think) is 8,064 bytes. (This is the kind of thing you can learn when you use a product like Ashampoo Uninstaller.

) Since uninstalling all Slysoft applications then reinstalling them in release order from oldest to newest fixed the problem, I feel this is a likely conclusion (but is still a guess).