Trying to replace the motherboard in a laptop is equivalent to trying to perform a heart transplant on your dog. Don't do it. Take it in, and when they tell you it'll take x hundred dollars to fix it, take it out, sell it on Craigslist/eBay, and start saving for another computer.
FWIW, I'm typing this from a used iBook G3 that's working, so it's not necessarily an issue of buying second hand. Appears you just had bad luck with this particular book.