Ouch, sorry to hear about your PowerBook. Here's a few tips to get your PowerBook running on an external display without using the built-in 12" LCD screen.
First you need to hook up an external monitor to your PowerBook, now plug in a USB keyboard or mouse. Then put the PowerBook to sleep. When the PowerBook is asleep and the lid is closed click the external mouse or press the space bar on the external keyboard. This will cause the PowerBook to wake up and disable the built-in LCD screen. The PowerBook may get warmer than usual but, once it disabled the LCD screen you can open the lid to help it cool off.
Hope that works 😀