Looking for the name of an old NES game?

Trying to relive my childhood, and really actually find the music theme it played. I can't remember the exact title, but I remember the introduction was basically of a kid sitting in his room or something like that, and he hears something in his backyard, some type of alien perhaps, or something like that, and all of a sudden, there's a hole in his backyard and he slips and falls down into the Earth, and somehow gets suited up and fights. Can't remember what he was fighting.. aliens, perhaps? It was only 1 player.

I don't think it's Mega Man.

Also, extra credit: There was another game that I can't remember, but you got to be an ostrich or some bird and you could jump high and you could kill things, I think, by shooting or jumping on them .. I forgot the rest. It was two players.

It was not Duck Hunt or Bubble Bobble.

Hopefully someone can figure it out. Thanks!