In order to understand and to promote the educational integration and utilization of Information and Communication Technologies (ICT), teachers need to be investigated in-depth, as substantial determinants of the educational process, and research interest ought to be concentrated on the factors that are inhibitory to their decisions concerning the pedagogical employment of ICT. Therefore, the present paper examines three interrelated factors that prevent primary school teachers from making use of computers and of other new technological means in their workplace. Through qualitative methodology and individual structured interviews, seven (7) teachers from public primary schools of equal number, in the prefecture of Magnesia, Greece, report a) the main problems encountered in the educational use of computers, b) their beliefs about the pedagogical value of the utilization of computers in the teaching process, and c) the "official policy" of their school of service regarding the usage of computers in instructional practice. According to the findings of this study, among others, a) the quantitatively and qualitatively inadequate or insufficient school infrastructure and technical support are ascertained, whilst highlighting b) the positive learning outcomes of the said use of computers, along with schoolteacher beliefs in favor of their confined employment. Finally, c) a range of existing school policy is observed, including the formal or informal encouragement of the voluntary use of computers, or the absence of corresponding guidelines. Overall, despite their limitations, the abovementioned results can be applied to pre-service and in-service teacher training, and in the formulation of the associated educational policy, taking into account the available national financial resources.