|"I don't think anyone specified if it was AC..."|
Your Topic title is:
Compaq Presario laptop AC jack
"It was the flux burning off that caused the smoke."
In normal circumstances, the jack in the laptop should not have gotten hot enough to burn off the flux.
If the jack was replaced by someone who did a proper job, the fault is probably with the AC adapter's cord near the DC plug, or with the DC plug itself - that's the most common thing that gets damaged - # 2 is the jack in the laptop. That's most commonly caused by people pulling on the cord rather than the plug when they unplug the AC adapter from the laptop.
If the battery was charged sufficiently, at least the minimal amount required for the laptop to boot, the laptop should boot anyway. Does it?