Reactivate dried up ink of ballpoint pens
As ink typically consists of non-polar dyes dissolved in a non-polar liquid, I would recommend using a straightened paper clip and a drop of acetone to clear out the dried ink clogging up the ink cartridge. This works by agitating the dried ink, as well as by replenishing the ink's solvent. Just be careful to not make too much of a mess!

Another method I have seen work before is heating the end of the pen under a flame, which melts the ink clogging the tip. For this method, my advice would be to not hold the pen in one place for too long, lest you risk melting the plastic.