I would still try to go back to samsung directly. They may be more receptive... it certainly won't hurt to try. After that, you are likely going to have to get your "hands dirty" to get anything done.... by taking off the back and accessing some of the electronics to do some checks. The first of which would be gently removing and reconnecting all the cables going to the main board and tcon boards. It possible that the cables may have been marginally seated and over time have become an issue... my fingers would be crossed...
After that, my first guess would be the TCon has an issue... alternatively, the main board may be also considered.... absent of any information about various electrical testing. The Tcon is responsible for signal timing and connection to the panel while the main board is responsible for conversion of signals and creation (ie. menu, apps, hdmi, analog video, etc).
Does the screen display work if just a menu is displayed? Is the issue across all inputs / sources including over the air, internal media apps?