I confirmed the basics of the configuration multiple times. Twonky Media was enabled. Each share was flagged as sharing all media file types. I restarted the service, rebuilt the database, rescanned the device. Nothing changed. After googling, I discovered I could connect to the NAS box with ssh. There were many recommendations to do this, rename two files, then restart Twonky Media. I did so with no change in behavior. However, after a little digging, I discovered a problem with the Twonky Media configuration. Once I changed that, everything started working.
The steps I followed were:
Login to the MyBook Live at http://mybooklive/UI/login
Enable SSH at http://mybooklive/UI/ssh
Connect via ssh (username = root, password = welc0me)
cd /CacheVolume/twonkymedia
vi twonkymedia-server.ini
change contentbase=/ to contentbase=/shares
save and exit
restart twonky at http://mybooklive:9000/config under Maintenance
Depending on your network, browser and ssh client, you may need to use a numeric IP address rather than "mybooklive". If you use Windows and don't have an ssh client, I recommend putty, which is what I used.