I'm reaching my limit here (I do small electronics) but that cap looks like it's on the primary side of power in, so it's rated for power line in. (Hence the high voltage rating).
What is the tv doing/not doing? If any of the LEDs (power led) turn on at all, I would guess that it's not that side of the circuit. (I don't know much about TVs, but these are always the questions I ask for troubleshooting)
Edit: looking at the debris near that part, something went. is the fuse okay? Is the mess localized around there?

