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Is the tv plugged into the wall, directly, or do you have it going into a surge protector?
And it is exactly 5 times, every time and then it works. How long will it work after that? Does this only happen when it has been off for a long period of time, such as over night?
LOL. No that will not be my answer.
It is likely an issue with the main transformer inside the television itself. Of course, this is something that needs to be repaired by a professional since there is a latent charge in the TV that can be dangerous if you open it up yourself.
However, before you do that, I would get a can of compressed air and blow out all of the vents and areas on the back of the TV. Pull it out from the wall a bit too. Then try it again. You may just have some dust issues causing the short.
Let me know if you have more questions.
I don't know the actual part numbers of your television (I tried finding the service manual online). Check your manual, if you still have it. Sometimes they will have a parts blowout diagram.
You are looking for either the main transformer (basically the thing the outlet plug runs into) or there is also a fuse in the TV that is meant to prevent excessive damage in the case of a power surge (I believe its called a pico fuse). You may want to replace that first, as it will be cheaper.