Bifunctional vinyl-terminated poly(dimethylsiloxane) chains are end-linked by tetrafunctional tetrakis(dimethylsiloxy)silane cross-linkers to produce irregular polymer networks with controlled stoichiometric imbalance and extent of reaction. The results are used as input to create comparative, nominally the same, three-dimensional Monte Carlo computer microstructures. Stress relaxation laboratory measurements and bead-spring molecular dynamics (MD) simulations are performed to estimate the relaxation shear modulus. It is found that the MD estimates reproduce quite well the measured equilibrium shear modulus G, despite the strikingly different time scales of measured and MD relaxation moduli. However, it is also seen that for near-stoichiometric networks the classical affine network model (ANM) gives equally good predictions of G. Additional MD simulations with phantom strands and regular networks are carried out. It is demonstrated that the ANM success is accidental since it is based on the fortuitous cancellation of two unrelated inaccurate assumptions of regular defect-free polymer networks and phantom strands that can freely pass through each other and themselves. Several contemporary theories of the elasticity of ideal Gaussian polymer networks are considered, and it is demonstrated that none of them is particularly suitable for predicting the shear modulus of the studied end-linked polydimethylsiloxane (PDMS) networks. It is shown that by taking into account the effects of trapped entanglements, reasonable qualitative and, at times, even semiquantitative predictions can be achieved. However, because of the ambiguity problems in the empirical fitting of the effective concentration of trapped entanglements, the resulting theoretical predictions are overall notably less accurate and less reliable than those obtained with the coarse-grained MD simulations that automatically account for the uncrossability of network strands. This emphasizes the incompleteness of the current theoretical descriptions of the effects of entanglements on the elastic behavior of irregular end-linked polymer networks with various values of the extent of reaction and stoichiometric imbalance and also suggests using our validated Monte Carlo microstructures to further study these effects.