Okay, the technical reason and how to do this properly.
The cable has become partially dislodged. The cable plugs in on the left side (button down) about 3" from the bottom. It has a friction clamp that is suppose to hold it in place. If the iPad gets jarred on it's left side, the cable has a chance of coming out. It only takes 1mm to cause issues. Jarring on the right side can reseat the cable.
If you think about the physics, when you jar it on the right side, the cable (which is loose) has a chance of slipping back into the connector using the weight of its own connector.
The safest way to do this is to drop on to a padded, but hard surface on the right edge of the iPad 2 from about 3-4". Hold it between your fingers so it only bounces on that right edge. I have a padded leather case it is in, so I just used a table on mine. I used carpeted floor on another. Since there is very little risk to damaging anything, this process can be done several times as needed.
The proper fix would be to remove the screen (see youtube videos), but that carries the higher risk of damaging the screen.