Backlight will turn off no display after short time

That would probably be the back light inverter board failing. It will eventually stop completely.
When it is off or out you should still see a ghost like image. It is possible the problem is the actual backlight but they tend to be out and stay out while the inverter or power board goes out after something on it heats up enough.

As a rule of thumb on these you need to check the repair costs against the price of a replacement tv. This type of repair/problem is common to any lcd display regardless of brand or type of device.What you have to watch for is that the repair cost isn't more than the replacement tv is worth. I'm not familiar with that brand so I can;t give you any hard numbers. If the inverter board is a separate board then it should cost about $50. If it is part of the main board then you can easily be $450. And yes the repair parts can/will cost more than a complete new tv. If you were to build a tv out of repair parts you would pay 3-5 times what the entire tv is worth.

So you want to check out any tv repair shops, check out if you have warranty and check out what the repair depot charges. Then do a bit of window shopping so you know what a new tv is worth. Use those numbers to decide if you want to repair or replace. The prices on new tv is dropping and if you watch for sales you may be able to get a bigger newer one than what you have.