New integral field optical fiber spectroscopy obtained with the INTEGRAL system, together with archival HST WFPC2 and NICMOS images, has been used to investigate the ultraluminous infrared galaxy (ULIRG) IRAS 17208-0014, one of the coldest and most luminous objects in the IRAS 1 Jy sample. We have found that the optical nucleus is not coincident with the true (near-IR and dynamical) nucleus, but that it is displaced by 1.3 kpc (1.5") from it. As a consequence, the previous optical spectral classifications for the nucleus of this galaxy have to be changed from H II to LINER. The ionized gas emission is concentrated around the optical nucleus, where a young (5-6 Myr), massive [(3+/-1)×108 Msolar], and luminous [(6+/-2)×1010 Lsolar] starburst is detected. Contrary to what is found in dynamically young ULIRGs, no strong line emission tracing star-forming regions, or tidal dwarf galaxies, is detected in the inner parts of the tidal tails. The two-dimensional gas velocity field identifies the optically faint K-band nucleus as the dynamical nucleus of the galaxy and shows that the 3 kpc, tilted (i~35deg) disk is rotating at Δvsini=250 km s-1. Radial motions of gas are found along the minor kinematic axis, which, according to the geometry of the system, are well interpreted as inflows perpendicular to the inner disk. The existence of such inflows supports the idea that, as a consequence of the merging process, gas is channeling from the external regions, several kiloparsecs away, into the nuclear regions where the massive starburst reported above is taking place. The kinematical, morphological, and photometric evidence presented here supports the idea that in IRAS 17208-0014 we are witnessing a luminous, cool ULIRG that is at the final coalescence phase of a system composed of two spiral galaxies with m<=m* and a mass ratio of ~2:1, each consisting of a disk+bulge internal structure, that have been involved in a prograde encounter. This system will most likely evolve into an intermediate-mass (~L*) elliptical galaxy. The multifrequency empirical evidence gathered so far shows no trace of a luminous QSO and indicates that starbursts dominate the energy output in this galaxy. Therefore, IRAS 17208-0014 does not follow the behavior expected in the ``ULIRG-to-QSO'' evolutionary scenario proposed by Sanders et al., but it supports the one recently proposed by Colina et al., in which two low-mass disk galaxies would produce luminous, cool ULIRGs that would not evolve into QSOs. The present study illustrates some caveats to bear in mind when studying high-z galaxies lacking two-dimensional spectral information of adequate linear resolution and shows that near- and mid-IR integral field spectroscopy is needed to derive the relevant astrophysical quantities. Based on observations with the William Herschel Telescope, operated on the island of La Palma by the ING in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. Based also on observations with the NASA/ESA Hubble Space Telescope (HST), obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under NASA contract NAS 5-26555.