I picked up this TV with the issue of having a dim right half of the screen. Brightness controls did not do anything. I had fixed a TV with a similar issue here.
The power supply part number BN44-00440A is hidden within the serial number and this post on badcaps.net indicates a potential cause is a failed capacitor CP811. I measured the voltage across one of the big filter caps and it was only 160V DC (should be around 380V DC). This reading indicated the backlights were not getting full power. The original part is 220pf/1KV so it may be better to replace it with a higher rated voltage (2kv or 3kv).
I pulled out the capacitor and put it in my ESR tester and it tested as a 0 ohm resistor so it had shorted out. When I replaced it and powered up the TV, the backlight came on at full brightness.