Thinkpad 420 battery not charging despite of Cells inside are good
In addition to checking voltage on the cell's pairs, you should try to load them with a resistive load (say, 4 &Omega;), and see if all sections holds any charge for longer than several seconds. 

Your comment that "windows shows 100% charged" means that the battery has reached the termination voltage (4.2V per cell), maybe too soon, and the battery management electronics likely indicates the fault to OS. It usually happens when some section of the battery develops high ESR and doesn't hold much of charge.

Smart batteries are very smart, they have coulomb gauges, and count battery cycles and remaining state of health. If the battery software/firmware thinks that the battery is bad, the laptop will refuse to charge the battery. You might want to look into this answer and into an example of smart battery IC BQ8050 to appreciate the complexity of modern battery designs.

I am afraid your battery has reached EOL and needs to be thrown into recycling bucket. Some cells might be still good enough to be re-used in DYI projects.