I feel like a total idiot. Kimmo's E-Mail brought me onto the right track. But instead of trying to disappear into a hole in the ground for embarrassment, I'm posting this in case anyone else has the same problem.
It just so happened, that my computer change requiring a new Rainlendar installation and importing the information from the old calendar, came in a time period where I had no
firm appointments or birthdays to remember for the next two weeks
. THEREFORE there was nothing displayed. I checked this by changing the "number of future days the list shows" from 7 to 16 in the Rainlendar Advanced Options, and sure enough, the next events showed up.
Much thanks for the nudge in the right direction and the help