In this work, we report on simulations of double-stranded DNA (dsDNA) ejection from bacteriophage φ29 into a bacterial cell. The ejection was studied with a coarse-grained model, in which viral dsDNA was represented by beads on a torsion-less string. The bacteriophage's capsid and the bacterial cell were defined by sets of spherical constraints. To account for the effects of the viscous medium inside the bacterial cell, the simulations were carried out using a Langevin dynamics protocol. Our simplest simulations (involving constant viscosity and no external biasing forces) produced results compatible with the push-pull model of DNA ejection, with an ejection rate significantly higher in the first part of ejection than in the latter parts. Additionally, we performed more complicated simulations, in which we included additional factors such as external forces, osmotic pressure, condensing agents and ejection-dependent viscosity. The effects of these factors (independently and in combination) on the thermodynamics and kinetics of DNA ejection were studied. We found that, in general, the dependence of ejection forces and ejection rates on the amount of DNA ejected becomes more complex if the ejection is modeled with a broader, more realistic set of parameters and influences (such as variation in the solvent's viscosity and the application of an external force). However, certain combinations of factors and numerical parameters led to the opposition of some ejection-driving and ejection-inhibiting influences, ultimately causing an apparent simplification of the ejection profiles.