Theoretically speaking, ‘MacBook Pro won’t turn on’ problem usually relates to one of two things. Either the display is malfunctioning, which means the computer is on, and you just can’t see that it is. Or there is some kind of power-related issue that is preventing it from turning on as expected.
The below steps you need to take to fix your MacBook Pro 13″ A1278 if it won’t turn on when pressing the power button.
Step 1：Power Button Power Up Testing
Step 2: Keyboard And Trackpad Testing
Step 3：MacBook Disassembling
Step 4: Motherboard Superficial Inspection
Step 5: Maintenance Drawing Referring
Step 6: Motherboard Voltage Testing
Step 7: Resistance Testing
Step 8：U5701 IC Replacing
Step 9: Assembling and Testing
Step 10: Keyboard Replacing
Step 11: Assembling and Testing
Step 12: Final Fault Diagnosis
Related article souce: https://blog.rewatechnology.com/how-...-wont-turn-on/