Heck no! You keep it and put a smaller, working TV on top of it.
Seriously, I've never had to dispose of a TV, but do you know of any special requirements for having it picked up with your usual garbage collection? Let them take it and deal with it.
What Leila said. Here in L.A. there are even services that pick up old TVs and computer monitors for proper disposal. Never simply toss one in a dumpster.