Pen won't write though plenty of ink

This solution works. You will need a very thin wood skewer, toothpick width, or a piece of thin firm wire about 8 inches long. Don't use a wide skewer. You will also need a paper towel.
Remove the cartridge from the pen. Carefully pop off the little end cap opposite the ball.
Insert the skewer into the cartridge. It should have plenty of play, and not squirt ink out the back end. Insert it all the way to the ball end (but don't push hard). When fully inserted, swirl it and twist it, to stir up the ink. You may get a little airbubble out.
Remove the skewer (it will have a lot of ink on it), and wipe off with paper towel.
Return the little end cap. Put back in pen.
Make circles on some paper, until ink flows freely.

There are a couple reasons a pen refill won't start writing right away. The first thing to check is the tip--often there is a bit of glue or plastic over it in order to prevent leaking.
If that doesn't work, then try one (or both) of the following two methods:
1) Place the refill (but not the tip) in some warm water. Heat will allow the liquid in the gel pen to become thinner and flow more naturally.
2) Hook a rubber band around the middle of the pen, using tape to ensure safety, and wind the pen while holding the rubber band on either side of the pen. Make sure the cap is on the pen. When the rubber band is tight, when you pull straight out on the rubber band from both sides of the pen, it should spin very quickly. The centripetal force will cause the liquid in the pen (at least half of it) to move toward the tip.
Make sure you fasten the rubber band to the pen with tape or something similar; otherwise the pen may go flying off at someone nearby. Also, again, make sure the cap is on to prevent any ink spraying out--this is unlikely in a gel pen, but it could happen.