One of my ink pens doesn't work properly. It is the most expensive pen which I have with me. There is a kind of ball inside that stops the ink from flowing, and the ball can't be removed. How can I get this pen to work?

Assuming the ball is made of some metal, this would mean that when you begin to write it falls to the lip of the cartridge and blocks it. If so, then this might help: Curl up a small wire piece into a small ball (small enough to go into the cartridge but with enough gaps between the wires for ink to leak) and insert into the cartridge so the metal ball cannot com to the lip of the cartridge to seal the flow of ink. Be careful when you dispose the cartridge as you can then reuse this wire-ball into the new cartridge. Note that the wire should be of high grade steel so that it does not react with the ink.