* If it is clean then the displays LVDS cable needs attention.
* If the external shows the same thing the GPU logic on the logic board needs attention.
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=== Update (02/18/2018) ===
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Most likely you'll need to replace the LVDS cable from the display to the logic board. Here's the IFIXIT guide to get the display off so you can gain access to the cable: [https://www.ifixit.com/Guide/MacBook+Pro+15-Inch+Retina+Display+Early+2013+Display+Assembly+Replacement/17045]. Once you have the display off you can slide the black clutch cover off to gain access to the connection on the display. Here's the cable you'll need: [https://www.thebookyard.com/product.php?cPath=39_368_349&products_id=14598|Retina MacBook Pro 15" Hinge, Left - LVDS cable - Apple P/N 818-2882]
What does an external display show?
* If it is clean then the displays LVDS cable needs attention.
* If the external shows the same thing the GPU logic on the logic board needs attention.