There are two possibilities:
1) The screen is warped, (Manufacture defect)
* Would explain why when you press down on parts of it the lines go away. Your re-aligning the internals to make a solid connection.
2) Faulty Digitizer, (Manufacture defect)
* Same as the first reason, but it is generally caused by the hardware IO’s chip giving a crappy signal.
Firm bet is on number 1 though.
Call the manufacture and see if they still have it under warranty, if it is not, you can replace the screen cheap.