If I roll no successes on a raid will my ship be destroyed to make up the difference, or does it just sit there and my turn ends?
If you roll zero successes and the defense value is 4 then you take 4 damage. This might sink your ship or it might not. Whether or not it sinks your ship, the raid was unsuccessful.
This seems clearly spelled out, step by step, under "Completing an Endeavor & Fortune".