ipad crashes after fresh install

I bought a used ipad version A1459 (so ipad 3 32G with wifi and cellular).

I set it up as new but the apps (all of them) continually closed after just a few seconds (even settings)

When on the home screen it would jump to the multitasking screen and back without being touched.

So, I tried recalibrating the home button (thought it might be sticking) and I also reinstalled as new a couple times,

then reset from DFU.

Even in the brand new install with no apps except the default ones, the apps close and the home screen jumps to the multitasking screen.

If this is a hardware problem, what is the problem?