How do I connect to a ground wire with no ends?
Thanks for the picture.  I have dealt with this many times.  It looks as though there is just enough slack in those ground wires to remove the copper crimp used there (forget what these are called) and add a ground wirenut.  The ground wirenut's are green and have a hole in the top to allow a new or existing ground wire to continue out.

So in your case....


remove the crimp with a pair of diagonal pliers
get a peice of spare ground wire several inches long
put the new piece in the top of the ground wire nut and push it in so it sticks to just about the base
twist the wirenut to the existing three ground lines, tying all 4 grounds together (the 3 existing and the new one coming out the top) 
Connect the new ground line coming out the top of the wire nut to your fan