First results are presented of an empirical modeling of the Earth's inner and near magnetosphere (X ≥ -15 RE), using a new set of data and new methods, described in a companion paper. The modeling database included 5-min average B field data, taken in a wide range of altitudes and latitudes by the International Solar Terrestrial Physics spacecraft Polar (1996--1999) and Geotail (1994--1999), as well as by earlier missions, ISEE 2 (1984--1987), Active Magnetospheric Particle Tracer Explorers (AMPTE)/CCE (1984--1988), AMPTE/Ion Release Module (1984--1986), CRRES (1990--1991), and DE 1 (1984--1990). To take into account the delayed response of the magnetosphere to the solar wind and interplanetary magnetic field (IMF), each data record in the data set was tagged by a trail of 5-min averages of the IMF, solar wind, and Dst field data, covering the preceding 2-hour interval. The axisymmetric ring current (SRC) and the partial one (PRC), both parameterized by the corrected Dst* index and the solar wind pressure Pd, were found to vary in strikingly different ways. While under quiet conditions the PRC is much weaker than the SRC, it dramatically grows in magnitude and rotates to the dusk sector with rising |Dst*| and Pd, significantly exceeding the SRC even during moderate storms, in excellent agreement with recent particle simulations. The innermost part of the cross-tail current is quite sensitive to the southward IMF and yields ~90% of the tail's contribution to the Dst index, in contrast with the more distant tail current, which responds mainly to the solar wind pressure and provides no appreciable contribution to Dst. In response to southward IMF conditions, Region 1 and 2 Birkeland currents rapidly grow in magnitude and expand to lower latitudes, while their peaks shift slightly in local time toward noon. The coefficient of the IMF penetration inside the magnetosphere was found to dramatically increase with growing IMF clock angle: while quite small (~0.1) for northward IMF, it rises to ~0.6 as the IMF turns southward. Priorities and challenges for future data-based modeling studies are discussed.