Macbook randomly shuts down?

This only happens sporadically, which actually worries more than if it was a common problem. About 3 months ago, my mac started having a problem where it would power up for about 2 minutes, then the screen's backlight would go out, leaving the mac on, but barely visible, and then it would go into sleep mode, and it would then shut off altogether. This problem lasted for about 8 hours the first time before it returned to normal, and a whole day the second time. The problem persisted even when the battery was taken out. I brought my computer into the Apple Store and they said they weren't sure what was wrong, but they replaced the battery, just in case. After that, my computer worked fine for the next few months. Just today, I got my mac back from a repair at the Apple Store, and it immediately started having this problem again. Does anyone know what might be happening, and what the right fix is? I also tried resetting every different thing that can be reset.

It sounds like the inverter or inverter cable may be defective or intermittent. Common problem on older MacBook Pro and MacBook machines. The cable snakes up through the hinge area from the inverter to the backlight. The next time the backlight goes out, try gently moving the top lid up and down slowly. See if it comes back on.