Laptop won't boot. Horizontal white lines at start and then it dies

Hi there.

I've recently done a factory reset on my mac that wouldn't load properly and it was working fine for a few days but today several applications failed to respond and when finder also failed I forced a shut down. Now I can't get it booting up again. At first it would start and there were purple horizontal lines over the apple logo and then it would restart and keep trying again and again until I forced a shut down. Now it has white horizontal lines and instead of restarting it will just shut off. I've connected it to an external monitor but it doesn't register - maybe because it never fully turns on. Fortunately I could retrieve my files via target disk mode.

Any ideas??