After no replies I decided to go ahead and venture into the world of flashing an ATmega16U2 chip to see if that was in fact the problem.
If you are a newbie to micro-controllers like I am, this is not a venture for the faint of heart. There is a lot of information online that is outdated and will trip you up, programs recommended that will not load on your PC, and other roadblocks that will frustrate the daylights out of you. However, if you are tenacious like me, and won't take "no blinks" for an answer, then you are in luck. My problem must have been that the factory did not flash the ATmega16U2 USB chip on my Uno, or the firmware was corrupted. Either way, flashing the chip with the firmware got it working.
I'll share my humble solution using the necessary files already in Arduino IDE (Ver. 1.8.3) to use the Windows 32 Command tool to run avrdude. The regular members on this forum might chuckle, and offer a more sensible way, to do this. So be it. I did not have the benefit of such advice, and had little or no knowledge of how to do this. I had to use my logic, troubleshooting skills, and brute determination to come up with this workaround or hack.
I should first note that this process involves copying and pasting files in the Arduino Program Files, so you need to have administrator privileges on your PC. Also, you will need to change the file paths used below if you didn't use the default location for Arduino IDE.
There are 3 key files needed for this avrdude based approach, and apparently they need to be in the same directory. The avrdude.exe file would not find the avrdude.conf file or the needed hex file using this method until I placed them all in the same folder. The avrdude.exe file is located in C:\Program Files\Arduino\hardware\tools\avr\bin. That's the folder I chose to use in case avrdude.exe doesn't work as a stand alone file. I then copied the avrdude.conf file from C:\Program Files\Arduino\hardware\tools\avr\etc and pasted it into the \bin directory. I also copied Arduino-COMBINED-dfu-usbserial-atmega16u2-Uno-Rev3.hex from C:\Program Files\Arduino\hardware\arduino\avr\firmwares\atmegaxxu2 and pasted it into the \bin folder.
I used my USBtinyISP programmer to do the talking with Uno, connecting it to the 6-pin header next to the USB plug on the Uno board. I made sure I had the red #1 cable connected to the #1 pin on the Uno, the one with a white dot. I expect that this method will work with the other programmers otherwise supported by the Arduino IDE, since they all appear to be listed in the avrdude.conf file. You just need to call the device out in the execute command described below, using the proper ID for it. Provided that your device is recognized in Device Manager, it should work.
Now for the Windows System 32 Command tool. If you don't know how to open it, enter cmd in the Start menu search box, then click on it when it appears. Change the directory by pasting cd C:\Program Files\Arduino\hardware\tools\avr\bin at the command prompt and pressing Enter. When the directory changes, paste the following avrdude execution code at the command prompt and press Enter: avrdude.exe -C avrdude.conf -c USBtiny -b 19200 -p m16U2 -vvv -U flash:w:Arduino-COMBINED-dfu-usbserial-atmega16u2-Uno-Rev3.hex:i.
That flashed the ATmega16U2 firmware and got my Uno working. The USB serial device is now communicating with me...RX & TX leds blink!
I found Programmer's Notepad, a free download program like Notepad, instrumental in working towards this solution. It opens .conf files and will help to identify the ID codes needed to reference any other programmer or firmware file in the format required by avrdude.
Chuckle if you will, but my Uno is now working and I can move on with my project! (That would be the project I chose to use the Arduino for, not the project of getting the Arduino to work.)
