Try this -- unplug all your HDMI connectors on the TV set and turn it on. Does it now stay on?
Darken the room, stare at the TV screen when you press the power button. Does your LCD screen light up then shut off within 2-3 seconds of it lighting up? Or is it lit longer than that?
It stays on, but says 'no signal' in the middle of the screen.....
Cables are unplugged, but it was longer than 2-3 seconds.... The LG logo came up, then it attempted to connect for 2-3 and powered down. Currently it is still on (cables unplugged) but stating no signal!
Ok to research your problem further, we do need to get the TV's full model number.
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There should be a sticker on the back of your TV set showing the short version and the "product code" version of your TV's model. Can you get that?