Since wireless sensor networks (WSNs) have been designed to be deployed in an unsecured, public environment, secured communication is really vital for their wide-spread use. Among all of the communication protocols developed for WSN, the Security Protocols for Sensor Networks (SPINS) is exceptional, as it has been designed with security as a goal. SPINS is composed of two building blocks: Secure Network Encryption Protocol (SNEP) and the "micro" version of the Timed Efficient Streaming Loss-tolerant Authentication (TESLA), named µTESLA. From the inception of SPINS, a number of efforts have been made to validate its security properties. In this paper, we have validated the security properties of SNEP by using an automated security protocol validation tool, named AVISPA. Using the protocol specification language, HLPSL, we model two combined scenarios-node to node key agreement and counter exchange protocols-followed by data transmission. Next, we validate the security properties of these combined protocols, using different AVISPA back-ends. AVISPA reports the models we have developed free from attacks. However, by analyzing the key distribution sub-protocol, we find one threat of a potential DoS attack that we have demonstrated by modeling in AVISPA. Finally, we propose a modification, and AVISPA reports this modified version free from the potential DoS attack.