This would be back in the 386 era of computing. It was a space game, and I'm pretty sure the world "Star" existed in the title (yeah, narrowed it down to about 10,000 titles). Basically, you picked a crew, and spent cash training them. YOu had stuff like a captain, science officer, comm officer, etc... You got a ship, and you could go through space. If your science officer had mad skillz, you could tell when someone was around and was going to go into a 'melee mode' where you communicated and did battle. You could run into police, or aliens. Depending on your comm & sci officer skillz, you could communicate with various aliens and such. Some were peaceful, some were hostile. There was lasers and torpedos for battle. You could land on planets (well, your science officer would have to scan it and if it was inhabitable by humans, you'd survive the landing), and could search around on the planet. If it was inhabitable, you could wire back to HQ and they'd give you money for finding it. Sometimes you'd lose a crew member on the surface and would have to replace him (or her) with another crew member until you got back to hq and replaced the person.
That's about the extent I remember. It was completely open ended and really a blast to play. The graphics were blocks and nothing was really that clean (used to think it was star control 1, but the graphics in star control are too nice to be the game I'm thinking of). It was the closest game that resembled 'star trek' I've ever played. Meet aliens, discover new worlds, no missions, just exploration and stuff... anyone have a clue what it is??