Since you can see fine on the external monitor, then your attached display, or the ribbon cable that connects it, are your problem.
If you feel comfortable opening it up (and it isn't under warranty) then you try replacing the cable and/or display yourself.
However, if it is under warranty, don't open it up. Contact the manufacturer about a repair. If it is not under warranty, and you don't feel comfortable doing the work yourself, then try a local tech.