LG 47LN5750 TV has no back light issue-

Hi there. I would advise you to unplug your tv from the wall. Wait approximately 5 minutes. Hold down the power button on the tv for 15 seconds without the tv plugged in. This is what they call power cycling. If plugging back in the tv does not work; you might have a power board issue. A typical power board/circuit board repair runs from $25 to $125.

1Check power board capacitors if swelled then replace them ,
2 check led output voltage at connector on power board. If voltage down come back from led penal then one or more leds fused.
Please replace it.
3 it may caused power board defective too.

LG TV 47LN5750 Backlight Out

you can get replacement parts at:
Lg 47LN5750 UH TV Parts

Have you checked your power supply voltages?...if so what are they?

The backlight is not working. Either power supply or led's

Sounds like Back - light problem.Check and replace damaged component/s at its back-light inverter board, or replace this board as card basis.If you wish to get some details; check the site linked here.Surf the site with patience.Pull up older posts.It will be best to replace the inverter board as card basis.
http://electronicshelponline.blogspot.com/
To some model sets; especially LED back-lighted types; the back-light inverter circuit will be part of the main power supply board [SMPS].In such cases, the power supply board might need replacement.To some models sets, the back-light inverter and SMPS section circuit will be integrated at its main board itself.If so; the main board should be replaced. To some models of sets, all these section circuit will be integrated at its main board.If this is the case, you have to replace the main board.

The TCON board or the LCD panel is faulty. Can confirm By replacing the TCON board
If you wish to get some details; check the site linked here. Pull up older posts.
http://electro-medical.blogspot.com/

What you are describing is common in these sets. The power unit tends to cause the LED backlights to fail. It is a 50 dollar parts cost but you have to upgrade the firmware to prevent it from happening again

Back - light problem? Check and replace damaged component/s at its back-light inverter board, or replace this board as card basis. If you wish to get some details; check the site linked here. Surf the site with patience. Pull up older posts. It will be best to replace the inverter board as card basis.
http://electronicshelponline.blogspot.com/
Some model sets; especially LED back-lighted types; the back-light inverter circuit will be part of the main power supply board [SMPS]. In such cases, the power supply board might need replacement.

time to take it in for a proper diasgnosis and then to decide if to fix or not