This most likely points to a mechanical lens problem, not a sensor issue. Based on the symptoms, the lens barrel may not be extending fully or evenly, possibly because it’s tilted or obstructed. That would also explain the black corner: part of the lens or lens-cover blade may be intruding into the frame.

Letting the battery run flat while the camera was on is unlikely to have caused the damage by itself. A weak or failing battery is a small outside possibility, though, since insufficient power can sometimes prevent a compact camera lens from extending completely. If practical, try a fully charged known-good battery first.

Also inspect the lens barrel carefully for grit, damage, or anything physically blocking extension.

If the lens is mechanically damaged or decentered, repair is usually uneconomical on an older compact camera like this. In most cases, replacement is the more realistic option unless the fault turns out to be just a battery or minor obstruction.