The error is coming from this block of code in Mail::Sendmail:

        unless ( socket S, AF_INET, SOCK_STREAM, scalar(getprotobyname
+ 'tcp') ) {
            return fail("socket failed ($!)")
        }
[download]

What this means is that the error occurs when the system is creating a socket, but before it attempts to connect to anything.

Are you running fedora? This sounds like a problem with SELINUX preventing the script from creating a socket.