No Disks Detected (RND4000-200NAS)

Solution found:

The cheap external power supply I bought off of Amazon failed in some strange way (it must have been producing enough power to light most everything up, but the drives spinning up must have drove the voltage low and it failed or something electrical that rhymes with that).

I bought a whole additional case off of ebay, but it turned out all I needed was the power supply.

There was actually another thread that I found which suggested that this could be a power issue but they suggested plugging the unit into a different outlet.  I didn't make the connection that it could have been the external power supply or think that the power supply could even have a failure mode where it started to not produce enough power rather than just failing outright.