We present an improved event-level likelihood formalism for including neutrino telescope data in global fits to new physics. We derive limits on spin-dependent dark matter-proton scattering by employing the new formalism in a re-analysis of data from the 79-string IceCube search for dark matter annihilation in the Sun, including explicit energy information for each event. The new analysis excludes a number of models in the weak-scale minimal supersymmetric standard model (MSSM) for the first time. This work is accompanied by the public release of the 79-string IceCube data, as well as an associated computer code for applying the new likelihood to arbitrary dark matter models.