Implementing alphabetical search in Magento can be tedious if you dont know the right approach. But its as easy as anything. You just need to alter two files to make it work.
Note: Do not edit or add this code to your core files if you wish to upgrade Magento to newer versions in the future. Please create below mentioned files in the app/core/code/local directory with complete directory structure as in Magento core.
app\code\local\Mage\Catalog\Block\Product\List\Toolbar.php
public function setCollection($collection)
{
$this->_collection = $collection;
$this->_collection->setCurPage($this->getCurrentPage());
// we need to set pagination only if passed value integer and more that 0
$limit = (int)$this->getLimit();

