OK, I figured it out myself and am posting to help anyone else who might
encounter the same problem.

I had been deleting them by marking the first, then holding the shift key
and selecting the last on a given page and hitting the delete key.  The
apparancy was that none were being deleted, because there were so many, but
in fact they were being deleted.  Problem was, doing it one page (screen
view) at a time would have taken weeks!!!

I turned on the Status bar and saw there were over 58,000 records (only
about 600 weren't blanks).  I selected the first, then using the scroll bar
slider, moved it about one column's worth and, holding the shift down,
selected the last one on the resulting page.  There were so many the
selection took a few seconds!  I then hit the "delete" key and kept my eye on
the count on the "Status Bar" the count went down by 10,000 or so!  So it was
working.  I repeated this until all the blanks were gone and I was back to
just populated records.  It only took a few minutes.

Hope this helps someone!