The popping-and-shutting-off problem occurs if either backlight is disconnected. If the system doesn't boot at all, then yes, as others have said there are several possibilities: 1) the lower screen backlight cable is loose or damaged 2) the upper screen backlight cable is loose or damaged (the tiny one in the top of the housing) or 3) the speaker cable is loose or damaged (connector p7 on the motherboard)
However, if, as in your case, the system does boot and the issue occurs mainly when you open the console up from the closed position, the speaker ribbon cable is actually torn, not just loose. There will be a tear in it that just barely breaks one of the conductors on the outermost edge of the ribbon cable. When the console is fully opened the tiny tear is stressed and the connection is fully broken, causing the system to shut off. When the console is closed or opened gently it may work for a time because the tear is not being stressed and the connection would still be complete, but only tenuously. The problem will get worse over time though. If you open the system up the tear will be large enough to see easily if you remove the speaker cable and lay it out flat. Whenever I get these consoles for repair and look at the speaker cable I'm always astonished they work at all with such severe tears in them.
As The Real Jdbye said though, it's not your LCD. The LCD wouldn't cause the system to shut off. If the upper LCD ribbon cable were bad the system would still boot, but you simply wouldn't see anything on the top screen. It wouldn't be the lower screen backlight cable either since that one is located in such a way that it would never become damaged via ordinary use.
tl;dr version is: replace the speaker cable. It's likely torn.