Particles with no weak, strong or EM interactions are not only perfectly consistent with the non-detection of dark matter in direct detection experiments and the non-detection of DM at the LHC. They are also consistent with the absence of any compelling DM annihilation signature. So, while non-detection of DM in those channels is parameter bounding for DM theories, it certainly doesn't rule out DM that is "sterile" (i.e. that only interacts via gravity) or DM that only interacts with other DM in addition to gravity.
The trouble is that the amount of correlation between inferred DM distributions and baryonic matter distributions is too tight to be explained by gravity alone and the shape of the DM distributions aren't what we would theoretically predict if DM was truly sterile or only interacted with other DM. So, truly sterile DM or DM that only interacts with other DM isn't enough to explain the phenomenology.
This leaves you looking for a fifth force that predominantly governs DM-ordinary matter interactions (and possibly also DM to DM interactions), such as the paper described below, in a dark matter particle theory.
Andres Olivares-Del Campo, et al., "
Dark matter-neutrino interactions through the lens of their cosmological implications" (November 14 2017).