Order-of-magnitude anomalously high intensities for two-electron (dielectronic) satellite transitions, originating from the He-like 2s(2) 1S0 and Li-like 1s2s(2) (2)S(1/2) autoionizing states of silicon, have been observed in dense laser-produced plasmas at different laboratories. Spatially resolved, high-resolution spectra and plasma images show that these effects are correlated with an intense emission of the He-like 1s3p 1P-1s(2) 1S lines, as well as the K(alpha) lines. A time-dependent, collisional-radiative model, allowing for non-Maxwellian electron-energy distributions, has been developed for the determination of the relevant nonequilibrium level populations of the silicon ions, and a detailed analysis of the experimental data has been carried out. Taking into account electron density and temperature variations, plasma optical-depth effects, and hot-electron distributions, the spectral simulations are found to be not in agreement with the observations. We propose that highly stripped target ions (e.g., bare nuclei or H-like 1s ground-state ions) are transported into the dense, cold plasma (predominantly consisting of L- and M-shell ions) near the target surface and undergo single- and double-electron charge-transfer processes. The spectral simulations indicate that, in dense and optically thick plasmas, these charge-transfer processes may lead to an enhancement of the intensities of the two-electron transitions by up to a factor of 10 relative to those of the other emission lines, in agreement with the spectral observations.