Removing second copy of ctools module from filesystem
Unless you have apc.stat = 0, then APC caching is likely not the problem.  You can always set apc.enabled = 0 as a temporary measure until you get the problem fixed.

What version of Drupal?

If you are on Drupal 7, you could try deleting the extra copy and then running Registry Rebuild via drush.  Follow the instructions on the project page.

The other method that should work for Drupal 6 and 7 would be to take a database backup, and then hand edit the {system} table.  If it has both "sites/all/modules/coots" and  "sites/all/modules/contrib/coots" in it, delete out the contrib entries.  If it just has the "sites/all/modules/coots" entries, edit them to take out contrib.  Then manually clear out all of the cache tables.

Make sure you backup your database no matter what you do.  Both of these are dangerous operations.