well, it could just be broken,
But, it could be the sensors inside being stuck, which will cause it to flicker in and out, or the video connections. There is a "nightstand" trick you can try, get a solid table/object and kind of hit the edges of the ipad perpendicular to the table. There is also "the hammer" method, which *i* have never used, but it seems to be the same thing.
http://www.youtube.com/watch?v=xwmk2id4x84
those are the easy diy fixes. The apple store is usually pretty legit on their estimates if you take it in, and won't charge you 500 bucks to fix a $400 toy. That said, its the apple store, so ya know, there is that...
If you wanna get hardcore you can actually crack it open, but i wouldn't bother unless you really know what your doing. Lots of people have success with the non-apple repair places too, like i-fixit or whatever. They usually have the most common parts on hand and fix them in a day.