I don't see any visible damage based on the images you presented. I see you're able to power it on long enough to install coconutBattery. Does the crash occur randomly or is it triggered by certain types of events? Does it occur after extended use? Does the device feel hot or very warm to the touch when it powers down? Have you checked for any crash logs in the Console utility? Was the fan dusty when you opened it? Does the crash still occur when you're booted in Safe Mode? Once you have some answers to those questions we can try to help you further. Good luck!