Cosmological hydrodynamical simulations as well as observations indicate that spiral galaxies are comprised of five different components: dark matter halo, stellar disc, stellar bulge, gaseous disc and gaseous halo. While the first four components have been extensively considered in numerical simulations of binary galaxy mergers, the effect of a hot gaseous halo has usually been neglected even though it can contain up to 80% of the total gas within the galaxy virial radius. We present a series of hydrodynamic simulations of major mergers of disc galaxies, that for the first time include a diffuse, rotating, hot gaseous halo. Through cooling and accretion, the hot halo can dissipate and refuel the cold gas disc before and after a merger. This cold gas can subsequently form stars, thus impacting the morphology and kinematics of the remnant. Simulations of isolated systems with total mass M~10^12Msun show a nearly constant star formation rate of ~5Msun/yr if the hot gaseous halo is included, while the star formation rate declines exponentially if it is neglected. We conduct a detailed study of the star formation efficiency during mergers and find that the presence of a hot gaseous halo reduces the starburst efficiency (e=0.5) compared to simulations without a hot halo (e=0.68). Moreover we find cases where the stellar mass of the merger remnant is lower than the sum of the stellar mass of the two progenitor galaxies when evolved in isolation. This suggests a revision to semi-analytic galaxy formation models which assume that a merger always leads to enhanced star formation. We show that adding the hot gas component has a significant effect on the kinematics and internal structure of the merger remnants, like an increased abundance of fast rotators and an r^(1/4) surface brightness profile at small scales.