Dave writes, "I have an old PowerBook G4 laptop with a broken monitor (it just displays vertical lines). I connected it to my HDTV using an HDMI cable and a DVI to HDMI adapter and all I got on my TV was a blue screen. I had the TV set to the right input. Any ideas?"
Connecting an external display to a MacBook or PowerBook, as you did when you connected your HDTV, typically causes the Mac to extend the desktop to the external display. Sometimes this doesn't happen automatically, which means you need to make manual changes. In your case, the Mac shouldn't try to use the built-in laptop screen because it's broken, but the Mac probably can't detect that. Fortunately there's a relatively simply solution to the external display problem you are having.
By default, Mac OS X assumes you want to extend your desktop to the external monitor, as opposed to mirroring what would normally show up on the built-in screen. You need one extra piece of hardware to get around this - an external keyboard.
Since you can't see anything on the broken screen, you obviously don't need to use it.
Instead, what you want to do is connect the external monitor or HDTV as you already did. Then connect an external USB keyboard and close the Mac. This tells Mac OS X that you are using external hardware and won't cause the Mac to go to sleep when you close it.
If you already paired a Bluetooth keyboard with your Mac, that will also work, but you won't be able to see the configuration screen if you haven't paired it. Keep in mind, you will also want a mouse, since you won't have access to the trackpad while the Mac is closed.