Deleted lines 61-63 of tpl_modules_shipping_estimator.php
Code:
    <label class="inputLabel" for="state" id="stateLabel"><?php echo $state_field_label; ?></label>
    <?php echo zen_draw_input_field('state', $selectedState, zen_set_field_length(TABLE_ADDRESS_BOOK, 'entry_state', '40') . ' id="state"') .'&nbsp;<span class="alert" id="stText"></span>'; ?>
    <br class="clearBoth" />
That got rid of the extra state field, but still did not allow the estimator on the shopping cart work. That did, however allow the popup shipping estimator to work. I would really like to get to the bottom of this, and get the estimator back on the shopping cart, rather than a popup window.