For those of you who might be interested in this issue, I was unable to find the reason for the problem, however, I did find a somewhat painful workaround.
First I'd remind you that I imported several hundred users from an external database using the PowerImportExport module.
I also had set a required profile for login on the site.
Then using the newsletter core module I sent out a blast e-mail was not sent to any of the imported users, even though they had a role as Registered Users.
The workaround was to edit the profile on each of these users (I didn't have to make any change). I was then able to send all Registered Users a blact e-mail which when to all Registered Users. Apparently, the import failed to set some interal data flag.
Thank you to those who offered their assitance with this issue. Your time and suggestions are appreciated.