Stephen writes:
   /* Bind anonymously to the LDAP server. */
   rc = ldap_simple_bind_s( ld, NULL, NULL );

I think that still Binds with LDAP version 2, which the server
may be rejecting.  Try to set LDAP version 3 first:
  int protocol = LDAP_VERSION3;
  ldap_set_option( NULL, LDAP_OPT_PROTOCOL_VERSION, &protocol );

Yes, that was it.
   if ( rc != LDAP_SUCCESS ) {
     fprintf(stderr, "ldap_simple_bind_s: %s\n", ldap_err2string(rc));
     return( 1 );

That only prints a textual representation fo the error code.  It does
not print the diagnosticMessage which the server may have enclosed to
answer your question.  Try ldap_perror(ld, "Bind failed");

Implementing this results in a very useful error message confirming your guess...
Bind failed: Protocol error (2)
    additional info: historical protocol version requested, use LDAPv3 instead

Thank you for your helpful reply