wasn't it Taylors ship they fished out of the lake? Brents had been badly damaged in the crash
I guessed which ship it was, but that's hardly the issue. Either way, those capsules weren't meant to launch on their own, but to be the nose cone atop a huge Saturn booster. The PotA film series is full of frequent retcons, each sequel having to ignore and rewrite the facts of the previous films to make its existence possible, but the implication that the tiny manned capsule atop the rocket was suddenly able to launch itself into orbit without help was one of the most implausible changes. And having the Enterprise on hand to help them escape the dying planet would've been the perfect way to fix it, if the writers had thought of doing so.