There is probably a microscopic crack in a conductor. This assumes that the techies who checked it over made sure that all connectors were properly seated. You can check by seeing whether the computer starts reliably after leaving it in hibernate in a place where the temperature is low (like a cool store) for an hour or two. Then try the same after leaving it in a very warm place (> 30 deg C) and check for start up trouble. Often very small cracks close up at low temperatures. The main thing is to see whether the problem is temperature sensitive.

The two beeps signify that there were errors upon boot-up and the system board couldn't initialize all hardware. I would be willing to bet that its the video card and what you have experienced comes from moving the unit. There is most likely a bent piece, frame, thermal displacement arm, or something else that dislodges a component when closed and transported. The problem is that you couldn't tell which one it is without knowing how much of an angle these pieces are supposed to sit naturally.

Does the laptop sit evenly on all four corners? If it doesn't, even the slightest bit this can be the problem. Also, after it was assembled after this first happen did it beep at all when restarted? Or did nothing happen? If this is a temperature issue (as expressed in the previous post) this could be a combination of problems not easily solved.

The computer does sit on all fours, but when I go to my girlfriend's a boot it up from hibernate, it starts up fine.  And then I come back to my room after shutting it down and set it on all fours, it will not boot up at all.  And after the computer guys reassembled the computer, it appeared as if nothing had happened; it still did that same two flashes and two beeps.  Perhaps they missed something critical, but they did not find any cracks in the motherboard and everything was reseated as far as they told me.

As far as I know, this reproduced the error.  I removed the hard drive (the two beeps seem to signify that there is no boot device) and I disconnected the ribbon cables to get the video.  So I guess the IDE cables from the hard drive are bad or the hard drive is bad and the ribbon cables or the video card is being twitchy.  Does this seem correct?

With the two beeps "No boot device found" should appear on your display. If you have no display then I would refer back to the video card as the primary faulty device.

 

It is also possible that one of the connectors to the HDD was stressed as there aren't any cables into the MB, it is a hard plug that comes out from the motherboard. This problem is equally so with the videocard, it could be good but the connectors are stressed causing the intermittent problem that goes away after everything has been reseated.

Problems like this are very hard to trace as they don't show themselves in any obvious fashion. In the short run, I would turn this into a 'desktop' unit and use a thumb drive to carry information back and forth. Also, look into having it more thoroughly looked over by a laptop tech so they can test the connections and find out if it is the video card or the motherboard.