As for what became of the Stargazer between the battle with the Ferengi and "The Battle"? Canonically we have no idea, "The Buried Age" by our very own Christopher covers this very nicely. in the book the ship was overly contaminated by radiation when the crew evacuated and the auto-destruct system failed.
Ugh!! Yet another instance of the auto-destruct failing. That excuse has been used so many times on screen it's ridiculous. While I haven't read the book, I hope the circumstances surrounding the failure of the auto-destruct was a little more creative than the computer voice simply saying "auto-destruct is offline."
I haven't read it in some time, but from what I remember they didn't so much set the autodestruct as the antimatter containment was failing rapidly from the ships power grid collapsing.
They all took to the life rafts and assumed the ship would blow up itself but it successfully jetisoned the antimatter pods. Leading to the plot point of the Stargazer being flat out of antimatter and the ability to make her own in the TNG episode. And I think their detonation leading everyone to believe the ship had actually been lost.