Its not the satellites making it run hot its the Sony towers hes using as mains. And it hasnt overheated and popped dead.He never did answer my question as to what level hes listening at but you can overheat any receiver if you push it too hard. The solution is to not push it too hard.
What size is the tv? Its unlikely you can get it fixed at that price. You will most likely have to replace the whole HDMI board even if the ports are ok. If you can find the part and do it yourself it may be that cheap. But what if that doesnt fix it? Maybe take it somewhere and get an estimate on it.