Is there a solvent in which one could dip the point, assuming that the ink has dried around the ball or just inside the tip? Any other suggestions apart from shaking it or blowing down the ink tube?

John Heward, December 2009

soak the tip ends in warm water,then scribble on paper to try them you may salvage some (but not all)

wirecutterman, December 2009

I come from a long line of bodgers - my father used to refill his biro pens with "engineers-blue" paste thinned with meths and rammed into the tube with piano wire - I used to loosen a sticky biro with gentle heat from a gas lighter until they started making the ends from plastic!

I would suspect that your biros are not pens of outstanding quality and that you may have to live with premature failures.

Peccavi, December 2009