the following link may be useful if your concern is just the F11 option or the removal or PC angel:
if the laptop is receiving a good power signal in AC, then it is the battery which is bad. but if you need to jiggle the AC adapter on the power port just to get a good signal, then its the power port which is loose.
if the inverter was bad, it may not show video depending on the damage internally. it is possible that the LCD is not bad nor the inverter board...it is most likely due to a bad connection after the fall it suffered. you can have it...