Magento needs a version of the database which is not available on shared servers. Do a search on Magento (over all of Lunarforums). Are you on a VPS or dedicated? If so, you should be able to install the correct levels of MySQL and PHP yourself.
On a shared server, if your cPanel has an "enable PHP 5" button, just click it to switch to PHP 5.2.x. Note that cPanel will still claim to be PHP 4.4.9. You need to run
<?php phpinfo(); ?>to confirm the PHP level that you're actually at. Sometimes you need to disable PHP 5 and re-enable it via cPanel if it doesn't "take" the first time.