The development of environmentally friendly and energy-saving processes for recycling electronic waste (e-waste) is still relevant today. The research presented in this work relates to hydrometallurgy, namely, the electrochemical leaching of metals from e-waste under the action of alternating current (AC) into hydrochloric acid solutions of electrolytes, and can be used for leaching both noble and non-ferrous metals from secondary raw materials. The main object of the study was disintegrator-crushed mixed computer PCBs metal-rich powders with a particle size (d) of <90 µm. The impact of such leaching process parameters as temperature (Tel) and composition of the electrolyte solution, AC density (i) on the electrodes, experiment duration (tex) while maintaining a constant electrolyte temperature (60 °C, 70 °C, and 80 °C) on the metal (Au, Ag, Cu, Al, Ni, Pb, Sn, Ti, Zn, and Fe) leaching efficiency has been studied. In addition, under similar experimental conditions, but without external control of Tel, the kinetics of metal leaching from raw material powders obtained via PCBs single and double crushing in a disintegrator has been also presented. Comparison of raw material powders obtained from different batches of the source material showed both the variability of its chemical composition and the different kinetics of Au and Ag leaching under the same experimental conditions. The optimal conditions for pretreatment of the raw material obtained by single crushing in a disintegrator (CHCl = 6 mol·L−1, i = 0.88 A·cm−2, tex = 1 h, solid-to-liquid ratio—8.6 g·L−1 and without external control of Tel) were determined. It has been shown that this electrochemical pretreatment is accompanied by transition of only base metals into the electrolyte solution, making it possible to significantly reduce their concentration in the final solution. Under pretreatment conditions, the following degree of metal leaching (RMe) has been established: RCu = 98.2%, RAl = 62.8%, RNi = 53.4%, RPb = 93.2%, RSn = 98.0%, RTi = 88.5%, RZn = 61.6%, and RFe = 78.8%. As a result of a subsequent two-hour electrochemical treatment of a solid residue, the degree of leaching of gold and silver was 73.6% and 86.7%, respectively. The presented results provide a broader understanding of the possibility of using the proposed electrochemical hydrochlorination method for noble and base metals leaching from waste PCBs. The novelty and practical value of this research is a validation of the developed technology in laboratory conditions using the real batch of the PCBs. This approach may also be useful to researchers involved in the recycling of other types of secondary raw materials.