The Return of Ishtar

The Return of Ishtar is an arcade game that was released by Namco in 1986. It runs on Namco System 86 hardware and is the sequel to The Tower of Druaga, which was released two years earlier. It was also the only Namco game that required a second player to play it, given that their three previous games that'd allowed two players to play simultaneously (Sky Kid, Sky Kid Deluxe, and Toy Pop) could also be played alone. It was the first game from the company to have a password feature to give players the opportunity to continue from where they left off after getting a gameover, but it was also their first to not feature a scoring system.

Story
This storyline is taken from the game's attract mode (if you wait through the two attract room sequences before inserting a coin):

GIL the Golden Knight went off to the tower to defeat DRUAGA. There are many monsters waiting there, as well as traps. But GIL overcomes the obstacles courageously. The Goddess ISHTAR saw GIL fighting and compassionately provides GIL with powers to defeat DRUAGA. And GIL fights on with the help of the shinning (sic) Blue Crystal Rod, to defeat DRUAGA and seal DRUAGA's magic power with the Ruby Mace. Because DRUAGA's magic was disspelled, GIL's lover KI could return to human form. And the tower which was restored by DRUAGA's magic power, returned ruins again, so the exit could not be found. The original resident of the tower, QUOX the Dragon, went back off to his dwelling because DRUAGA's magic was dispelled. But other monsters lost the powers that controlled them, and became more fierce, and kept on wandering inside the tower. Although they had defeated DRUAGA, the world was still sealed in darkness. To save the world, GIL and KI must take out the Blue Crystal Rod, which is the center of the power of Goddess ISHTAR safely out of the tower. The world is waiting for "The Return of ISHTAR" © 1986 NAMCO