There are three things inside your TV that could cause this... the power cord (least likely), the line fuse (likely), or the power supply circuit card (most likely).
The power cord is pretty self-explanatory... if you swap it out and the issue persists, the cord isn't the issue. A new one is relatively inexpensive, or you can use an ohmmeter to check it and you won't have to buy one as long as it's good.
The fuse is a bit more involved. You'll need to remove the TV's rear panel and trace the input power cord to a circuit card... that's the power supply board; it will be fused... check/replace the fuse(s). Replacements should be available at local retailers like Radio Shack or online at mcmelectronics.com, digikey.com, or mouser.com.
If the power cord and fuses are fine, you should replace the whole power supply board. You might want to hire a technician to do this... it's a fairly delicate process. If you need to find a local tech, just let me know... I'll need your zip code.
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