Removing the battery won't solve anything, if the laptop in question won't work without a battery inside it. Try replacing the battery (as it's the cheaper option).. If that doesn't work, perhaps the power supply is dead.
NOTE: Before replacing the battery, check the power supply thoroughly. Does it appear damaged? Bent connectors normally are broken off on the inside of the plugs, either where it plugs into the wall, or into the computer. Are there any splits, tears, or cracks in any parts of the wires used for the adapter? Also, is there a recall on the adapter/batteries in question?