A thorough understanding of future integrated fast-ignition experiments combining compression and heating of high-density thermonuclear fuel requires hybrid (fluid+particle) simulations of the implosion and ignition process. Different spatial and temporal scales need to be resolved to model the entire fast-ignition experiment. The two-dimensional (2D) axisymmetric hydrocode DRACO [P. B. Radha et al., Phys. Plasmas 12, 056307 (2005)] and the 2D/three-dimensional hybrid particle-in-cell code LSP [D. R. Welch et al., Nucl. Instrum. Methods Phys. Res. A 464, 134 (2001)] have been integrated to simulate the implosion and heating of direct-drive, fast-ignition fusion targets. DRACO includes the physics required to simulate compression, ignition, and burn of fast-ignition targets. LSP simulates the transport of hot electrons from the place where they are generated to the dense fuel core where their energy is absorbed. The results from integrated simulations of cone-in-shell CD targets designed for fast-ignition experiments on OMEGA [T. R. Boehly et al., Opt. Commun. 133, 495 (1997); C. Stoeckl et al., Fusion Sci. Technol. 49, 367 (2006)] are presented. Target heating and neutron yields are computed. The results from LSP simulations of electron transport in solid-density plastic targets are also presented. They confirm an increase in the electron divergence angle with the laser intensity in the current experiments. The self-generated resistive magnetic field is found to collimate the hot-electron beam and increase the coupling efficiency of hot electrons with the target. Resistive filamentation of the hot-electron beam is also observed.