A friend of a friend of mine has a calculator (ti83+) that, when bumped (not the keypad), garbage appears on the screen and the cursor changes position (from top to bottom, top to middle, top to half on top and half on bottom, etc.)

Also, the memory menu is a screen full of random garbage. I've tried resending the os and doing an all reset, nothing helps. I'm assuming that something is loose inside.

Any ideas what it could be? This just started one day when he was graphing something.

Something loose on the insides is the only thing I can think of, as there aren't any accelerometers or anything feeding data to the OS, so it can't be a software error if it only occurs when bumped

Open it up and look for something loose, then solder it back down...