Magento – Magento 2 display old price AND special price in category list

The price is pulled from catalog/product/price.phtml. The following code will get the lowest price of all associated simple products. This doesn't take in to consideration all of the tax rules in this file though. You could also change the variable $finalPrice in the below code to just be 0 and that would return the smallest amount that would be added on to the configurable.

// Load the full product
$configProduct = Mage::getModel('catalog/product')->load($_product->getId());
// Full product has to be loaded in order to pull configurable attributes
$configAttributes = $configProduct->getTypeInstance(true)->getConfigurableAttributes($configProduct);

// Get the configurable base price
$basePrice = $configProduct->getFinalPrice();
// Create an array to store attribute price values
$attributePrices = array();

// Loop through the configurable attributes
foreach ($configAttributes as $configAttribute) {
    // Grab the pricing information for the configurable attributes
    $simplePrices = $configAttribute->getPrices();
    // Loop through the pricing information for the configurable attributes
    foreach ($simplePrices as $simplePrice) {
        // Check if the additional price is percent or fixed of configurable price
        if ($simplePrice['is_percent']) /* Percent */ {
            // Calculate percentage using base price of configurable product
            $attributePrices[$simplePrice['value_index']] = ((float)$simplePrice['pricing_value'] * $basePrice) / 100;
        } else /* Fixed */ {
            $attributePrices[$simplePrice['value_index']] = (float)$simplePrice['pricing_value'];
        }
    }
}

// Create a array of all simple products associated to the configurable product
$simpleProducts = $configProduct->getTypeInstance()->getUsedProducts();
// Create an array to store simple price final price
$finalPrices = array();

// Loop through all the simple products
foreach ($simpleProducts as $simpleProduct) {
    // Create final price variable and set it to base configurable value
    $finalPrice = $basePrice;
    // Loop through the configurable attributes
    foreach ($configAttributes as $configAttribute) {
        // Get the value of the attribute for the simple product
        $attributeValue = $simpleProduct->getData($configAttribute->getProductAttribute()->getAttributeCode());
        // Get the price of the attribute from the price array
        if (isset($attributePrices[$attributeValue])) {
            // Add the value onto the final price of the simple product
            $finalPrice = $finalPrice + $attributePrices[$attributeValue];
        }
    }

    // Check if simple product is saleable before adding final price to our array
    if ($simpleProduct->isSalable()) {
        // Add the final price to the final prices array
        $finalPrices[$simpleProduct['entity_id']] = $finalPrice;
    }
}

// Gets minimum price of the array 
echo min($finalPrices);

Magento completely ignores prices of associated products in the configurable product type. You can specify a price difference for each associated product within a configurable product, but the base price and special prices are always taken from the configurable product itself.

Conclusion is: You cannot achieve what you try to do without custom extensions. There are some extensions around that change how pricing for configurable products work, but due to these substantial changes there are always rewrites of important core classes and you should think twice if you really need it.

This extension is a good example: Better Configurable Products

But you should not expect it to work out of the box, at least not if you use a custom theme. This is not a "one click install and forget" extension, it should be installed and configured by a developer.