Same issue. I sat down on couch, the moment I put MBP on my knees, it quit. I found that the cursor will stop moving as the failure begins, right be before beeps or shutdown.
Tried again, cursor quit, I rapped the back of the MBP lightly and it came back to life. I knew right there this is a mechanical issue. Digging online, one guy said the black screws retaining the RAM clips were too tight.
Santia delatorre above also has the solution, I used thin wall rubber tube chunk, pushed the clip back over the RAM stick…..that has to be done just right or it wont work. MBP would not start w/ the back removed, spring loaded pins in various places must be in contact with the aluminum back to start, after starting it can be removed, leave screws out. Rotate computer so display is flat on its back, watch the cursor movement while gently probing RAM stick on top, you can find right where the issue is. DO NOT touch anything electrically conductive with fingers. As suggested above, I cleaned RAM contacts, loosened 4 black screws SLIGHTLY, jammed tube in clip to push it over and retain RAM. When I started I could actually see the RAM stick was crooked, higher on one side than the other. So far so good. Thanks to all. Don’t panic.