The final analysis reveals that it was not faulty hardware, rather it was a configuration error.
The HP command line interface allows arbitrary length SNMP community strings to be entered. However, we are predominately a Cisco network, and we used many of the same settings on this HP switch. It turns out that the problem is that the HP switch will only boot if community strings are 16 characters or less. It will happily accept (and function) with longer SNMP community strings input via the command line as we do on our Cisco equipment, but it will get stuck in an initialization loop if it ever reboots.