Screen stays black - but MacBook working

I have a MacBook Pro 13" with retina screen from early 2013, Mac OS X. About six months ago the screen went completely crazy (white with bits of random colored stripes) after waking up from sleep mode. After a few hard shut downs it seemed to work again, but since then the screen stays black occasionally when turning on the MacBook. In that case I can still connect an external screen and it works perfectly, but it's like the MacBook doesn't recognize its own screen. I've tried both the SMC and PRAM reset, but no luck. The keyboard backlight always works, as does the keyboard itself (caps lock light comes on and off). This problems happens whether plugged in or not. The weirdest thing is that it sometimes works for two weeks, but then randomly decides to stop working.

An official Apple repair center in the UK thinks it might be the motherboard, which they can replace for 550 pounds - but then I'd rather buy a new one. What about the inverter cable / board?

Any help is much appreciated as I can't rely on my MacBook anymore.....