We bought the set 2 years ago. No timer countdown message. Yes, the light blinks. 11 blinks between pauses.
We did as you suggested and the same problem occurred. The tv stayed on for a count of 16.
The 11 blink code on this set indicates "Fan SOS", which means that the cooling fan inside the TV is not working. This is why the set only stays running for 16 seconds before shutting down, because the internal temperature sensor is shutting the set off. The solution is to have the Fan cleaned and lubricated or replaced. The average cost for having a shop do this is about $150 parts and labor, and the link below can be used to locate a tech:
If you're looking to do this yourself, or need further assistance let me know.
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Is this something we can do ourselves?
This is not something we are prepared to do at this time. Thank you