Trying to remember a Nintendo game

Hmm. Can you describe the game? Whatever it was, if it had the up-up-down-down code, then it was Konami game... that might help you narrow down your search.

Super Mario Bros. and Zelda are two of the NES games that I remember, along with Contra, thinking back to when my son got his first Nintendo back in 1988.

You'll probably find the name in one of these lists:

http://en.wikipedia.org/wiki/List_of_computer_and_video_games

http://en.wikipedia.org/wiki/List_of_cancelled_video_games

According to Wikipedia's List of Konami Code Games, here are the NES games that are known to use some version of the code:

Akumajou Special: Boku Dracula Kun
Contra
Crisis Force
Gradius
Gradius II
Gyruss
Life Force
NBA Give N' Go
Teenage Mutant Ninja Turtles II: The Arcade Game
Teenage Mutant Ninja Turtles III: The Manhattan Project
Top Gun: The Second Mission
Kid Klown in Night Mayor World
Tetris (version published by Tengen)
Tom and Jerry
Zombie Nation