Model lg42ln5700-uh. Why does it turn on, displays the LG logo, then turns off?

Sorry.... It was a lazy answer... at the end of a long day.

Your TV attempts to turn on, finds a problem, then turns off!
This is because the TV has a smart electronic power supply that can sense certain problems.
Like overheating or it senses excess current draw from other circuits.
Everything is fine until about the time the logo appears then shuts itself down.

First:
Check that the tv is getting ventilation.
No blocked air holes, as they use convection to cool the insides. Hot air out top, cool air in bottom.
Take a photo on your iPhone of the rear connections.
Remove all connections from rear in case they are adding to the problem.
Tap or slap the back a few times on startup to see if movement plays any part in the fault. Loose Connectors.

A modern tv works very much like a desktop computer.
No internal nobs or adjustments any more.
It's all CPU, Memory, Video memory on a circuit board.

If you feel comfortable with opening it up and checking inside then you might see the problem and be able to fix or replace a faulty module.
But... if the tv has just one large circuit board, thats little tougher to replace (& expensive)

Second:
With the back removed, check for loose connectors / wires,dust. Cockroach residue or nests, cause copper track shorts on circuit boards.
Follow the AC power lead to where it attaches to the electronics.
This will be the switch mode power supply.
This is where most modern electronics devices get their problems.
Look at the Electrolytic Capacitors on this board. The small round tin cans with an x on top.
Do any of them have a bulge in the top?
If so, the cap is probably Bad & needs replacing,
They also sometimes leak brown fluid from their bottom onto the printed circuit board.
You would either replace or repair this electronic module.
Turn Power On.... all working

Good Luck

Seehttps://www.youtube.com/watch?v=W8KTiFeN... Sorry.... It was a lazy answer... at the end of a long day. Your TV attempts to turn on, finds a problem, then turns off! This is because the TV has a smart electronic power supply that can sense certain problems. Like overheating or it senses excess current draw from other circuits. Everything is fine until about the time the logo appears then shuts itself down. First: Check that the tv is getting ventilation. No blocked air holes, as they use convection to cool the insides. Hot air out top, cool air in bottom. Take a photo on your iPhone of the rear connections. Remove all connections from rear in case they are adding to the problem. Tap or slap the back a few times on startup to see if movement plays any part in the fault. Loose Connectors. A modern tv works very much like a desktop computer. No internal nobs or adjustments any more. It's all CPU, Memory, Video memory on a circuit board. If you feel comfortable with opening it up and checking inside then you might see the problem and be able to fix or replace a faulty module. But... if the tv has just one large circuit board, thats little tougher to replace (& expensive) Second: With the back removed, check for loose connectors / wires,dust. Cockroach residue or nests, cause copper track shorts on circuit boards. Follow the AC power lead to where it attaches to the electronics. This will be the switch mode power supply. This is where most modern electronics devices get their problems. Look at the Electrolytic Capacitors on this board. The small round tin cans with an x on top. Do any of them have a bulge in the top? If so, the cap is probably Bad & needs replacing, They also sometimes leak brown fluid from their bottom onto the printed circuit board. You would either replace or repair this electronic module. Turn Power On.... all working Good Luck See https://www.youtube.com/watch?v=W8KTiFeN9k8