Cell Padding or Margins Within a Table

Greetings! I have a table with many cells containing text. The text is not
flush against the left border of the cells; there is reasonable space with
the text left-aligned. When I insert cells (a row at a time) into the table
and add text, that text is flush against the left border. All the text
settings appear the same. When I click within the original cells and check
the tab ruler, I see the indent sliders are just to the right of the blue
"partitions"; when I click within the cells I added, the sliders appear right
on the "partitions" and won't allow me to slide them to the left. I can't
move them in the Paragraph dialog box either.

Any suggestions?
Thanks,