Chosen Solution

Will not power on .. took it to Apple they checked battery and did reset and worked for a week .. and stop turning on again .. they checked battery and said it’s fine .. and want 600 to fix .. more then it’s worth . Any ideas

You may try popping off the bottom cover, unplug battery and then plug in MagSafe adapter, if system starts up on its own and works flawlessly it might be a battery issue you can try to resolve by replacing battery. If it doesn’t work then Apple may be right and you’d need to find a replacement logic board or find someone in component level repairs who may attempt fixing your system. Either way, we’d be very far from the 600$ bill you mentioned.