We have conducted a comprehensive mid-IR spectroscopic investigation of 67 Low Ionization Nuclear Emission Line Regions (LINERs) using archival observations from the high resolution modules of the Infrared Spectrograph on board the Spitzer Space Telescope. Using the [NeV] 14 and 24um lines as active galactic nuclei (AGN) diagnostics, we detect active black holes in 39% of the galaxies in our sample, many of which show no signs of activity in either the optical or X-ray bands. In particular, a detailed comparison of multi-wavelength diagnostics shows that optical studies fail to detect AGN in galaxies with large far-IR luminosities. These observations emphasize that the nuclear power source in a large percentage of LINERs is obscured in the optical. Indeed, the majority of LINERs show mid-IR [NeV]14/[NeV]24um flux ratios well below the theoretical low-density limit, suggesting that there is substantial extinction toward even the [NeV]-emitting region . Combining optical, X-ray, and mid-IR diagnostics, we find an AGN detection rate in LINERs of 74%, higher than previously reported statistics of the fraction of LINERs hosting AGN. The [NeV]24um /[OIV]26um mid-IR line flux ratio in AGN-LINERs is similar to that of standard AGN, suggesting that the spectral energy distribution (SED) of the intrinsic optical/UV continuum is similar in the two. This result is in contrast to previous suggestions of a UV deficit in the intrinsic broadband continuum emission in AGN-LINERs. Consistent with our finding of extinction to the [NeV]-emitting region, we propose that extinction may also be responsible for the observed optical/UV deficit seen in at least some AGN-LINERs.