We present ISO observations of the S(0), S(1), S(2), and S(3) rotational lines of molecular hydrogen from two molecular clouds near the Galactic Center (GC). We have also measured continuum dust emission at infrared wavelengths with ISO and the rotational radio lines J=1-0 of 13CO and C18O and J=2-1 of C18O with the IRAM-30m telescope. Using the dust continuum spectra and the CO lines we derive a total visual extinction of 15-20 magnitudes toward these GC clouds. After correcting the H2 data for extinction, the gas temperatures are 250 K and the column densities of warm gas are 2* 1021 cm-2. This is the first direct measure of the H2 column densities of the warm component; with this, we estimate an NH3 abundance in the warm gas of 2 10-7. The column density of warm gas is, at least, a factor of 100 larger than the corresponding column densities derived from the warm dust. The observed ortho-to-para ratio (OTPR) is 1, clearly below the local thermodynamical equilibrium (LTE) OTPR for gas at 250 K of 3. Low velocity shocks ( 10 km s-1) are the most likely explanation for the column densities of warm gas and dust and the non-LTE H2 OTPR.