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 ^ { 13 } CO and C ^ { 18 } O and J=2–1 of C ^ { 18 } O with the IRAM-30m telescope . Using the dust continuum spectra and the CO lines we derive a total visual extinction of \sim 15-20 magnitudes toward these GC clouds . After correcting the H _ { 2 } data for extinction , the gas temperatures are \sim 250 K and the column densities of warm gas are \sim 2 \times 10 ^ { 21 } cm ^ { -2 } . This is the first direct measure of the H _ { 2 } column densities of the warm component ; with this , we estimate an NH _ { 3 } abundance in the warm gas of \sim 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 \sim 1 , clearly below the local thermodynamical equilibrium ( LTE ) OTPR for gas at 250 K of \sim 3 . Low velocity shocks ( \sim 10 km s ^ { -1 } ) are the most likely explanation for the column densities of warm gas and dust and the non-LTE H _ { 2 } OTPR .