I have had the same issue with my Inspiron 5720. I got the first one at the end of December 2012 and with slight movement the display would go out into these static lines. You need to turn it off and restart to get it back. They have come out and replaced the LCD and cables, same issue. They returned and replaced the motherboard, same issue. They then replaced it with another 5720, same issue. They just replaced the motherboard on the new one, same issue. I am now fighting with them to have a different model sent to me. This is now a known issue with many reports of it on the Dell forum and they keep denying it. They have discontinued production of the 5720 also. Please feel free to contact me at firstname.lastname@example.org
and I will gladly share all of the sites I have found with reports of the same issue. I have also contacted the Better Business Bureau and am tempted to begin going further since I cannot do my work because this laptop keeps shutting down. Good luck.