Hm, I don't understand what a "new cpanel" refers to. Are they moving you to another server with the same domain name? Are they moving you to a different domain? Are you moving to a different host with the same domain name? Are you moving to a different host with a different domain name?
In all four cases transferring your site is dead easy: just use Akeeba Backup! Even the free (Core) version will do. The whole procedure is: install Akeeba Backup, backup your site, upload your site to the new host along with kickstart.php (a free download from our site), run kickstart.php, follow the instructions. You can't go wrong. There are a gazillion video and text tutorials out there to help you do that, as well as our own video tutorials and –of course– our Quick Start Guide.
Now, if you are moving to a different domain name (e.g. xyz.net to uvw.net) you will have to do one more step only if you are using the .htaccess Maker feature. Remove the .htaccess file from your site. Then log in to your site's back-end and go to Admin Tools, .htaccess Maker and scroll to System Parameters at the bottom. Change the two domain name fields to match your new domain name, then click on Save and Create .htaccess. Job done!
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!