We conduct extensive Monte Carlo simulations to investigate the factors that control the isotropic-to-nematic transition of hard colloidal polymers in bulk and under various conditions of confinement. Utilizing a highly idealized model, polymers are represented as linear chains of tangent hard spheres of uniform length, whose stiffness is controlled by a bending potential leading to rod-like configurations. Confinement is realized through the presence of flat, parallel, and impenetrable walls in one, two, or three dimensions while periodic boundary conditions are applied on the unconstrained dimensions. All simulations are performed through the Simu-D software, composed of conventional and advanced, chain-connectivity-altering Monte Carlo algorithms. We explore in detail how distinct factors, including chain length, stiffness, confinement, and packing density affect the isotropic-to-nematic transition exhibited by the polymer chains and identify with high precision the concentration range where this phase change takes place as a function of the applied conditions.