  [ABRIDGED] We analyse near-infrared integral field spectroscopy of the
central starburst region of NGC 1140, obtained at the Gemini-South telescope
equipped with CIRPASS. Our ~1.45-1.67 um wavelength coverage includes the
bright [Fe II] emission line, as well as high-order Brackett (hydrogen) lines.
While strong [Fe II] emission, thought to originate in the thermal shocks
associated with supernova remnants, is found throughout the galaxy, both Br
12-4 and Br 14-4 emission, and weak CO(6,3) absorption, is predominantly
associated with the northern starburst region. The Brackett lines originate
from recombination processes occurring on smaller scales in (young) HII
regions. The time-scale associated with strong [Fe II] emission implies that
most of the recent star-formation activity in NGC 1140 was induced in the past
35-55 Myr. Based on the spatial distributions of the [Fe II] versus Brackett
line emission, we conclude that a galaxy-wide starburst was induced several
tens of Myr ago, with more recent starburst activity concentrated around the
northern starburst region. This scenario is (provisionally) confirmed by our
analysis of the spectral energy distributions of the compact, young massive
star clusters (YMCs) detected in new and archival broad-band HST images. The
YMC ages in NGC 1140 are all <= 20 Myr, consistent with independently
determined estimates of the galaxy's starburst age, while there appears to be
an age difference between the northern and southern YMC complexes in the sense
expected from our CIRPASS analysis. Our photometric mass estimates of the NGC
1140 YMCs, likely upper limits, are comparable to those of the highest-mass
Galactic globular clusters and to spectroscopically confirmed masses of
(compact) YMCs in other starburst galaxies.
