The fine structure of multi-compartment neurons can simultaneously capture both temporal and spatial characteristics, offering rich responses and intrinsic mechanisms. However, current studies of the effects of channel blockage and noise on neuronal response states are mainly limited to single-compartment neurons. This study introduces an analytical method to explore theintrinsic mechanism of channel blockage and noise effects on the response states of multi-compartment neurons, by using the smooth Pinsky-Rinzel two-compartment neuron model as a case study. Potassium, sodium, and calcium ion channel blockage coefficient are separately introduced to develop a smooth Pinsky-Rinzel neuron model with ion channel blockage. Methods such as single-parameter bifurcation analysis, double-parameter bifurcation analysis, coefficient of variation, and frequency characteristics analysis are utilized to examine the effects of various ion channel blockages on neuronal response states. Additionally, smooth Pinsky-Rinzel neuron Subunit noise model and conductance noise model are constructed to investigate their response characteristics by using interspike interval analysis and coefficient of variation indicators. Subthreshold stimulation is used to explore the presence of stochastic resonance phenomena. Single-parameter bifurcation analysis of the ion channel blockage model elucidates the dynamic processes of two torus bifurcations and limit point bifurcations in Pinsky-Rinzel neuron firing under potassium ion blocking. Double-parameter bifurcation analysis reveals a nearly linear increase in the Hopf bifurcation node of potassium ions with input current, whereas sodium ions exhibit a two-stage pattern of linear decline followed by exponential rise. The analysis of average firing frequency and coefficient of variation indicates that the moderate potassium channel blockage promotes firing, sodium channel blockage inhibits firing, and calcium channel blockage shows the complex characteristics but mainly promotes firing. Subthreshold stimulation of the channel noise model demonstrates the stochastic resonance phenomena in both models, accompanied by more intense chaotic firing, highlighting the positive role of noise in neural signal transmission. The interspike interval and coefficient of variation indicators show consistent variation levels for both noise models, with the conductance model displaying greater sensitivity to membrane area and stronger encoding capabilities. This study analyzes the general frequency characteristics of potassium and sodium ions in a multi-compartment neuron model through ion channel blocking model, providing special insights into the unique role of calcium ions. Further, the study explores stochastic resonance by using ion channel noise model, supporting the theory of noise-enhanced signal processing and offering new perspectives and tools for future studying complex information encoding in neural systems. By constructing an ion channel blockage model, the effects of potassium and sodium ions on the frequency characteristics of multi-compartment neurons are analyzed and the special influences of calcium ions are revealed. Using the ion channel noise model, the stochastic resonance is investigated, supporting the theory that the noise enhances signal processing. This research offers a new perspective and tool for studying the complex information encoding in neural systems.