Most active galactic nuclei (AGN) lack prominent jets, and show modest radio emission and significant x-ray emission which arises mainly from the galactic core, very near the central black hole. We use a quantitative scenario of such core-dominated radio-quiet AGN, which attributes a substantial fraction of the x-ray emission to the presence of abortive jets involving the collision of gas blobs in the core. Here we investigate the consequences of the acceleration of protons in the shocks from such collisions. We find that protons will be accelerated up to energies above the pion photoproduction threshold on both the x rays and the UV photons from the accretion disk. The secondary charged pions decay, producing neutrinos. We predict significant fluxes of TeV-PeV neutrinos, and show that the AMANDA II detector is already constraining several important astrophysical parameters of these sources. Larger cubic kilometer detectors such as IceCube will be able to detect such neutrinos in less than one year of operation, or otherwise rule out this scenario.