Our dog chewed a blue ink cartridge on our cream, shag pile, wool rug.
 Any suggestions on how to get the ink out? Thanks.

Have you tried milk? I had blue ink on my wooden floor and by using
milk it dissappeared almost completely.

good luck :)

A professional carpet cleaning company could probably dye (or bleach)
the spot to match the rest of your carpet again. I doubt there is any
way to remove ALL the ink.

Kriswrite

Here are some possibilities:
://www.google.ca/search?hl=en&q=remove+ballpoint+pen+ink+stain&btnG=Google+Search

Once I had a Magic Marker that leaked indelible black ink into the
carpet. The stain was only about the size of a dime. After various
stain removers failed to fix the problem, I took a single-edged razor
blade and carefully carved out the discolored fibers. I then gathered
pristine fibers from elsewhere on the carpet, bundled them up, and
glued them into the area where the stain had been. This worked quite
well. If the stain is large, I doubt that it would be as good a
remedy, though.