When I start the machine the machine boots up but the screen is black.
I then reset the PMU and start up the machine and the screen lights up.
Now I have replace the internal battery and external battery.
Is the a PMU problem? The hinges were replaced a couple of years back.
Sometimes if I move the screen the machine will lock up.

If you look real close at the screen when it goes out, can you still make out an image like the brightness is turned down all the way? Another good test is pointing a flashlight into the Apple logo on the back and see if you see the image.

Well since I did my post, my machine is not having a problem booting. A couple of times it started up but froze on start up with a dark screen. I tried the flash light thing and there is no image.

Now I wonder if I have some kind of weird shorting problem. If I wiggle the laptop to much force the system freezes.

But the last three or four times the laptop has started up without a problem. So I must have some kind of intermittent problem.

Since this not my primary computer and I only use it from browsing and play a couple of old OS 9 games, I think I will just wait and see how long it take to completely die.

I think my problem is the PMU. I have left my laptop plugged in all of the time and it starts up just fine.
When I unplug the laptop from the power source, it starts up with a black screen. And there is no evidence of
anything on the display using a flashlight.

It is generally going to be the logic board with your symptoms but you may want to try a PMU first given the price difference.

I will keep you in mind. Right now I am not sure I will fix the Powerbook. Although someday it may be a collector's item since is one of the orginal Titanium G4's.