The laptop won't run without power supply. Battery is in good condition and charges. If I remove the power supply the laptop shuts down almost immediately. If i try to boot without the power supply connected the power led comes on and fan runs for a few seconds and stops. I then have to hold the power button until the led goes out in order to restart.
Sounds like your battery, while holding a charge, is not putting out enough power to run/start the laptop. That is a typical sign of the battery going bad and needing replacing. That would be the only fix, replace the battery.