Magento 1.9 Search – Magento 1.9 Search Not Working Properly

As i see you are trying to rewrite the model.so you have to have rewrite the model in the following way

<models>
    <catalogsearch>
        <rewrite>
            <resource_fulltext>Sid_Newsearch_Model_Resource_Fulltext</resource_fulltext>
        </rewrite>
    </catalogsearch>
    <newsearch>
        <class>Sid_Newsearch_Model</class>
        <resourceModel>newsearch_mysql4</resourceModel>
    </newsearch>
</models>

and importantly you are trying to rewrite wrong module which doesn't exists.your class should be

Your class under Sid/Newsearch/Model/Resource/Fulltext.php should be like

class Sid_Newsearch_Model_Resource_Fulltext extends Mage_CatalogSearch_Model_Resource_Fulltext

try avoiding folder called CatalogSearch under Model.

Open your file Mage_CatalogSearch_Model_Layer and in method

public function prepareProductCollection($collection)

before return $this;

Add following rows:

Mage::log($collection->getSelectSQL(1), false, 'search.log', true);
Mage::log((array)Mage::getConfig()->getNode()->global->models->catalogsearch, false, 'search.log', true)

(it's for debug purpose to understand your problem).

Then open your var/log/search.log and put result to your first post (there should be long sql query and array where we can see rewrites).