Ballpoint pens can stop working for several reasons
a) - ink has flowed away from the ball during (horizontal or even inverted) storage
b) - ink has coagulated so that the ball won't turn easily
c) - ink has coagulated to that it won't flow to the ball under any conditions
The thing is that you only find out if it isn't c) by trying the things that solve a or b first.
Heating the tip temporarily makes the ink (even gungy ink) more fluid and can help to restart a pen. However if the ink has flowed away from the tip there may be an airspace behind the ball and heat will expand that and push the ink further away.
Find someone willing to apply centrifugal force towards the writing end (ensuring the tip is covered, dahikt).
this is commonly how they eliminate a possible airspace in the factory. If you make up a support frame so that you can have a (balanced) arm assy that is put into a drill, ~1000rpm will push the ink against the ball even if it is fairly gungy. The longer the arm is, the higher the centripetal force at any given rpms. Be warned that if the refill comes out of the drill as it is spinning, it will fly like a dagger and will make a hole in anything (or anyone) that gets in its way....
cheers