I installed my refurbished amplifier today and problem solved. The instructions that came with the unit said that I should wait up to 5 minutes while the amp communicates with the radio, and the radio and the car had to be on during this test. So, I waited several minutes, then tried turning up the sound, and it worked!
I ended up getting my amp from my local Lexus dealer. I told them that I found an amp online for $495, and they gladly offered to match the price. Lexus backs the unit with a 12 month warranty. I might of been able to find an amp for less, but I was tired of messing around, I liked the warranty, and I was able to purchase locally.
Thanks to all for you support and assistance!