I had the same problem with a MacBook 2.0ghz Core2duo and the motherboard was faulty. I found a shop in Peterborough, Ontario, Canada to repair the motherboard for $200 CDN, now it's working great. My macbook had the same symptoms than yours but it worked well if connected to an external monitor. Also the battery was not detected by the computer and the isight web cam was not working. All these issues were repaired.