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Offhand the red light simply flashing and the set not turning on isn't outlined in the manual as it's a "hardware failure"- not a normal occurrence. This generally is caused by the Mainboard in the set failing and requiring replacement.
However it's worth it to try a hard reset, as sometimes the processor in the TV can simply have locked up.
The first thing you would try, is disconnect the set from power, then press and hold the power button on the TV itself (not the remote), for 10 seconds and release. Then plug the set back in, and also check that the power cord is connected tight at the TV as well. Press power once, and see if the set powers up normally. Try this procedure up to 2 times, and please let me know what happens.
Okay, I need to know if that light starts blinking as soon as the power cord was plugged in, or only after the power button is pressed please?
Then WHAT were you referring that "flashes" in your original post here?
"The red light came on the front of the TV, but when we push the power button on the remote (batteries in the remote were changed out just now), it flashes and the TV doesn't come on."
Sorry, so it's only the remote that flashes. The red light remaining on constantly indicates a failed mainboard.
Please allow me a few minutes to compose the diagnosis.
Could you please check the model number and confirm that it's actually: LED43A45RQ and not LED43C45RQ (the "C" being the difference)?