I had the exact same issue. Picture displays for about 10 seconds, then goes dark. I checked the voltages on the power supply board for VC-1 to VC-12, each was around 8 to 9 volts, but VC-2 was only around 3 volts! These 12 separate voltages feed 2 LED back-light strips, each consisting of 6 regions. I cut the track that supplies VC-2 to the back-light connector and now the screen stays on (with the exception of a dark spot on the bottom left due to region 2 not getting power).
Today I went through the removal of the back-light strips, but it's not an easy process and they can't be removed without destroying them. On top of many screws, there is also a fairly strong adhesive that binds the back-light strip to the edge of the thick aluminum back panel. Even to expose the strips, there's a thin metal strip that is held in place with screws and tucked in between the LCD panel and the aluminum back panel with some adhesive that needs to be gently removed. A lot of residual adhesive left over from the strips needed to be cleaned up carefully. Unfortunately heating the glue didn't seem like an option due to the thick aluminum back which would just act as a big heat sink, and the area needed to be heated is too close to the connectors for the LCD screen, so very tricky and easy to cause more damage.
I found the strips online for around $40 which I should get in about 2 weeks. Hopefully I haven't damaged anything else in the process. I got the TV for free so it's worth the gamble. I'll update on my progress.
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