Have you checked for water damage? There's a small piece of moisture-reactive paper in the bottom of the headphone jack, shine a light down there; if it's gone from white to red then there's probably water damage in there bridging something or what have you.
When my iTouch got wet in the rain it would sometimes press random spots on the screen.
Put it in the airing cupboard or on a radiator on not-too-hot and wrapped in a towel overnight. See if that helps.
Good luck. Costs loads to get them repaired.