Big thread, great advice.
I spent hours researching this problem on the net, and have settled for a chip on the logic board that, after a lot of wear and tear, doesn't make contact correctly with the mother board.
Apparently it is 'easily?' fixed by taking your mac to bits and inserting a plastic shim across the offending chipset....the pressure on the shim when you put the ibook back together is the fixer.
But if, like me, you don't have the `bottle' to start taking your ibook apart and messing about with metal across circuit boards, just get a pack of Post It notes, (I use the small 1.5?x1.75? ones), place your ibook on the pack on a flat surface, and press down on the left and right side as you switch it on.
Keep the gentle pressure on till you get through to the blue screen and all should be well. It's not a permanent fix, but it works and needs doing at each bootup. I'm happy doing it each morning, as I work from home, but it might ruin your author street cred if you have to do this in a cafe or public area.
If you only want to boot up to get your files off prior to sending it off for repair it might just be all you need.
I need to add that in 99 ex 100 cases this will work simply by placing the postit note pack in the middle of the case, under the ibook so that it balances, and switch on as normal. It seems the weight of the beast does the business without any undue pressure. Try that first.
How did my ibook begin to die? Worked fine for 4 years, then someone stole my bespoke ibook case, and I used an old pc one that was lots bigger than the case size. I think using that case and the constant bouncing around my car boot for hour upon hour as I travelled the country has loosened the board slightly.
Hope this helps at least one person out there.