I've had a similar case before, single black line, without the multiple thin ones you have.
In my case it was one of the line drivers gone defective (usually spread out over 2 PCB's on one side of the TV) sometimes they will burn a small hole in the top of the TQFP package, sometimes the PCB will fuse a power supply track leading to the defective driver IC, otherwise you'll just have to deduce which one is the culprit from the number of drivers and the position of your blank line.
In my repair notes I found that I had replaced a defective AN16021AA by a SN755866, a couple of years later the same TV came back with another dead AN16021AA.
Some PCB preheat is useful when replacing these IC's the PCB's usually have large ground planes to dissipate heat.