The Daedalus Encounter opens on a grim premise: Casey, a veteran space marine, survived a catastrophic accident only to have his body left beyond repair. His consciousness now lives in a life-support module aboard the Artemis, the ship he shares with fellow marines Ari (Tia Carrere) and Zack (Christian Bocher). Casey can interact with the world only through a small remote-controlled probe that emits light pulses and responds to yes/no prompts.
The war the three fought is over. Ari and Zack have become salvage pirates to survive. During a routine haul, the Artemis collides with a derelict alien spacecraft drifting on a collision course with a nearby star. Stranded aboard, the trio must explore the enormous ship — designated the Daedalus — and solve its many mechanical and laser-based puzzles to find a way off before they are incinerated.
Inside the Central Hub they find six hexagonal doors. Behind each lies one of six purple orbs; collecting all of them powers a dormant device that eventually reveals an elevator out. The vessel's remaining crew — hostile aliens called the Krin — flee the rising heat as the ship closes on the star.
The game ships three possible endings: the Artemis burns as the alien vessel reaches the sun; a surviving alien turns hostile, forcing Ari to destroy it and its offspring before Casey steers the ship clear; or the alien communicates with Casey, a force field appears, and an egg hatches into the alien Queen who, possessing race memory, repairs the Artemis and answers the crew's questions before sending them safely on their way.