Thanks to everyone for the great advice on how to solve the "No Lights, and Not Generating" problem on the Aqua Rite system.
I recently ordered the "Current Limiter Inrush 2 Ohm 25A" part# 570-1062-ND from Digi-Key, which arrived in 3 days. I ordered a spare and the total with shipping came to $5.74
The new Current Limiter (aka black thingy) looks identical to the one originally on my circuit board, including the writing on one side:
SL 32
2R025
Even though the original Current Limiter looked fine, I decided to attempt to replace it since the diagnostic panel showed very low numbers for Amps; and since, as predicted in this forum, several pool supply stores said that they can 'repair' my Aqua Rite but replacing the circuit board with a new one ($300). They confirmed they do not test or attempt any repairs to circuit boards.
With the circuit board removed, the back of the Current Limiter did show slight darkening, like a burn. Once I got the Current Limiter 'de-soldered' from the circuit board, it did indeed break apart in my hands. With the encouragement and information in this forum, I too as a first time solder-er was able to remove the old and replace with a new one. With the circuit board back in place, I turned the power on and the power light came on and the system is once again generating chlorine.
Thanks so much for all the input on this forum.