How were the backups from the other web host performed? If you simply downloaded the files you had on the other host and also took a backup of the MySQL databases (instead of say, taking a Home Directory backup of your account), upload your website files to the public_html folder on your account through FTP (or use cPanel's file manager to upload them to the public_html folder). For the MySQL databases, just go into phpMyAdmin and upload them there using the "Import" function.