I had the same problem with my iBook G4 1.2mhz. It had been working perfectly for years and then suddenly the screen started to go black and then cycle through the colors. It seems that it's a flaw in the manufacture/design of this computer that many iBook G4's develop sooner or later. The computer is long out of warranty and it was either fix it myself, spend hundreds fixing a machine worth half of that or use it for a large paperweight.
This article describes the problem and one possible solution.
http://www.coreyarnold.org/ibook/
Again, do it at your own risk and only if the symptoms fit your computer. If it doesn't work or it's botched your computer may be done, but if you have this problem it's pretty much done anyway.
I did not do the shim-job. But clamping the computer or torquing the body would get it to work, temporarily. It was a classic cracked/bad contact problem. Shim it, solder it or send it off for someone else to repair.
Instead of the shim solution, after the chip was identified, I got the SMALLEST soldering iron I could easily find (a 15 watt plug in model for about $9 at Radio Shack with a sharp point on it) and proceeded to heat up the pins on the chip to melt the solder and reestablish contact. I had to use a magnifying glass to do it and it was VERY precise work. I got the soldering iron hot and tinned the tip wiping off any excess solder. Too much solder or any additional solder and you'll bridge pins. I then just touched and drew the tip of the iron away from the body of the chip and toward myself. The first time I tried it, the computer worked pretty well for a couple of hours (a significant improvement), but then went back into the black and then solid color cycling screen. I thought maybe I hadn't given it enough heat and time and redid the process. Maybe a second or two on each pin, no more. Certainly no additional solder or it'll bridge the pins and short out and your computer will be even more permanently done than before. Using the magnifying glass I could see that the solder around the pin would change color. That's enough. Then draw the iron off the pin at right angles to the body of the chip. Then on to the next pin.
The second try was successful and I've had the computer on for hours with no crashes now, when before the fix it wouldn't run 3 minutes.
Disclaimer: do this at your own risk. You can use the shim system outlined above, but I believe that will only last temporarily and distorts the board causing more problems. I didn't dismantle the board but only removed the bottom and heat shield. So far so good. What do you have to lose with a machine that's not working that would cost you big bucks to repair otherwise?
My son in law had a 12" iBook G4 with similar problems. I did the same thing to his computer and it's now working well too. Thus far, two for two.