"Cheap logic board"? Hmm, I've had about eight logic boards replaced in my 800 MHz iBook, under the extended warranty, and the bill that Apple pays just for the part itself each time is always over $2,000.
It sounds like you need a new computer, as do I. I have a little more than a month before the 3-years-from-purchase date arrives, and my ninth logic board (counting the original plus replacements) smells like melted wax, so I know it's ready to die within the next two weeks. If Apple still refuses to replace my iBook this time and insists on one more logic board replacement, I'll scream at Apple Support on the phone. Americans don't have to endure more than three replacements, so why should Canadians suffer with such stubbornness?! I just can't figure it out.