We present a simple, low-cost, and low-power alpha-particle detection system for environmental radioactivity monitoring. The system exploits a previuosly-developed high- resistivity-silicon detector with internal amplification capability based on the bipolar-transistor (BJT) effect and readout electronics based on commercial IC's. Two-dimensional numerical device simulations are adopted to assess the feasibility of the BJT detector as an alpha-particle detector that can be operated, without losing its internal signal amplification capability, with floating base and low collector voltages, so that device technology can be kept simple, very small DC power consumption can be achieved, and a single 5-V power-supply voltage can be used for readout electronics and detector biasing. The charge amplification accomplished by the BJT detector allows a single, commercial chip to be adopted, to perform charge preamplification and 20-bit A/D conversion. The digital output is sent to a low-cost microcontroller that can be periodically interrogated through the IR port. The cost of the readout electronics is in the order of 60$ and it can operate with standard Li-ion battery for about 60 hours.