Finally got it working!
I uninstalled the audio drivers to start from scratch. Then, I installed the RAID utility V18.104.22.168 per this note on the TVAP page -- Special note for Qosmio G35 computer owners: Update the TOSHIBA RAID utility on your computer to V22.214.171.124 or higher before running this "Toshiba Value Added Package" update.
Next, I installed the TVAP exe. Finally, I installed the unmute exe. I saved all of them to the desktop and installed them "As Administrator". I did them one at a time and restarted the computer after each. So to recap the order was:
1. RAID Utility TOSHIBA RAID Utility V126.96.36.199
2. TVAP Model Content Page
3. Unmute Content Details
I hope this helps the next G35 user that lost their sound.