Chosen Solution
Same here. Late 2008 Macbook. I can only charge in Sleep mode, but if I leave the charger attached, Macbook will shut down within a couple of minutes. Can only charge in sleep mode to avoid blinking green lights. Must remove magsafe to run laptop.
Install this app: CoconutBattery paste a snapshot of the main screen with the MagSafe charger plugged in and one without here so we can see whats up. Heres how to paste them into your question: Adding images to an existing question