|Are you sure this laptop can run without a battery installed? I had a netbook fool me into thinking it had a monitor problem recently, but it was just an old battery that couldn't take more than a surface charge.|
Have you tried shining a flashlight in at the laptop monitor. It might indicate a bad backlight if you can see something.
Do you get an orange light or green light on your external monitor?
Both not working might indicate failure in the display circuitry on the motherboard.