Question: If I remove the battery & run from a power source will it lengthen battery life?

Answer: Laptop battery  have finite life spans. Whether you use the power cord and remove the battery it will lengthen the life of the DELL laptop battery .

Li-Ion  Dell Latitude C610 battery lifespan is approximately 1000 charge cycles, or 2-4 years under normal operating conditions.

Keeping the Dell 1691P battery  in a cool place can prolong its life but not in a period of extended storage. The Li-ion battery should be stored at 40 percent rather than full-charge state.

The battery ages even if not used. For best results, keep the Dell 75UYF battery cool. In addition, store the battery at a 40 percent charge level. Never fully charge or discharge the Dell Inspiron 700m battery before storage. The 40 percent charge assures a stable condition even if self-discharge robs some of the battery's energy. Most battery manufacturers store Li-ion batteries at 15°C (59°F) and at 40 percent charge.

Keeping a  Dell Inspiron 710m battery on constant charge is and never using it is not good for the laptop battery. Run the battery down and recharging it at least once every month.