Possessed TV - That's funny, some moron probably would buy it on Ebay. Here are my experiences with TV's turning on and off.
1) My family's TV: It did this for years. I mean YEARS. My parents finally went and got it fixed, I don't remember what they said the problem was. It wasn't the cord, and it wasn't remote control related though. Just something that happened. It would go days without doing it, then sometimes it would pop on and off 4 times in a row. Completely unpredictable. It sounded painful when it happened (I'd think "there's no way the TV is going to handle this long-term), but like I said, the TV lasted for YEARS doing this. Since getting it fixed a couple of years ago, the TV is still going strong.l
2) My TV. I bought it 4 years ago. It's a 27" Samsung (I think) from Circuit City. If you do anything that blows the TV's mind (like switching channels too fast or turning game machines on/off/on/off/on/off really fast) it will pop off and sometimes right back on. Not sure how the Cable/Antenna input could cause the TV to turn on and off but it's definitely related to the picture signal.
Hope this helps. In my experience with the two TV's it has never been a problem. You might want to get it checked out though, just in case there is something wrong with the cord that could be a fire-hazard.