That 15 minutes is stressful on the set and can lead to higher repair bills.
The old BAD CAPS (see google) is a typical cause for warm up issues like that. There's also many other non-user-serviceable causes but remove this from service to stop the damage.
When I turn it on, my LG 42lb5df LCD TV goes thru a distorted picture frenzy (screen blinking off/on, horizontal interference) for about 15 minutes before picture comes in. TV set does not turn off, just picture distortion. Seems to need to warm up??
Please ask questions for clarification. Thx

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