Can a digital cable box ruin a tv?

I think so...my digital cable box was REALLY warm to the touch. When I turned my TV on it played a few minutes then went out. We have had digital cable for about 5 years and no problem...but then the box never was hot either. I think something went wrong in the box and fried my TV. Can't prove it...but my TV was fine until the box heated up....then it didn't work anymore.