What laptop is it? Even if it's out of warranty ti would be worth contacting the service people if its a known brand such as Dell or HP - they may be able to point you in the right direction, even if you don't pay them to fix it
Otherwise, it's a real tricky one... I woulds have suspected gpu failure, except you say it works ok in safe mode.... Still, unless a change of driver fixes it, or you have a virus or other nasty involved, it looks to me like a hardware problem, which will take a proper repair to fix, the sort you would normally want to be under warranty for....