Fritz Weld @ edn.com proposes a simple circuit to check li-ion battery health. He writes:
Lithium-ion batteries are sensitive to bad treatment. Fire, explosions, and other hazardous condition may occur when you charge the cell below the margin that the manufacturer defines. Modern battery chargers can manage the hazardous conditions and deny operation when illegal situations occur. This fact doesn’t mean, however, that all cells are bad. In most cases, you can replace the discharged battery and increase your device’s lifetime. Figure 1 shows the circuit for testing battery packs.
Simple circuit indicates health of lithium-ion batteries – [Link]