Precision M4800 laptop: sudden shutdowns and freezes upon movement.

Lately, my Precision M4800 laptop (service tag: ), has been suddenly, and unprompted, been shutting down if I move it, like say picking it up a few inches off the table.  A similar problem happens if the Laptop is bumped or moved slightly, such as if my elbow bumps into it, or a turn or push it a inch or so too quickly, the screen will freeze up, with a bunch of randomly blinking rectangular tears appearing all over the screen, not to mention that it crashes at the same time.  Otherwise the Laptop runs like normal, I notice no performance issues or overheating, just that it has become extremely motion sensitive, so that, unless it is on a perfectly flat and stable surface, there is a good chance, even just on my lap, the a small motion will cause it to crash.  The Laptop is still under Warranty.