Thanks @Alex_h1 for your response.
I should have clarified that all the basic troubleshooting steps were taken such as:
- Apple TV was plugged in and turned on
- Internet connection was plugged directly to modem via Network cable and working (checked other apps to make sure the connection and upload/download speed was good)
- I signed out and successfully signed back into my Apple ID account on all my other devices (iPhone, iPad, iMac, Macbook)
- All my devices have been updated to the most current OS software release including my Apple TV
SOLUTION
After trying a few things, I determined that it is the (now mandatory) "two-step sign in verification" process that was causing the issue because Apple TV (2nd Gen) does not support two-step verification in the way other devices do. However, I figured out that if you request a verification code from another device, you can add that number to the end of your password and the Apple server accepts that and allows you to sign in.
For example, if your verification code is: 1-2-3-4 and your password Apple ID is: "password", then you combine the verification and your password and enter "password1234".
I hope this answer can help others who have the same issue now that Apple has made two-step verification mandatory across all devices (including older ones). Thanks again!