Almost every time there is a blank page on a php application, it denotes a php fatal error somewhere. It's not uncommon, it happens and there can be many reasons for it.
Troubleshooting tips
Error reporting
First of all, you have to enable Error Reporting, so Joomla/php will print any errors in your browser. This way you will get an idea of what's causing the fatal error.
Open configuration.php search for the line:
var $error_reporting = 'none';
and set it to:
var $error_reporting = 'maximum';
Refresh the page and see if now you get any error messages.
Different Environments & System Requirements
Usually, in cases like yours, where you are restoring a working site on a totally new environment that you just setup, this may be caused due to differences between the 2 environments.
The new environment might be lacking of important minimum system requirements that your site depends on. It can be the software versions like php, or required php extensions.
Corrupted Backup
Other possibilities is that your backup/restoration of files might be corrupted (e.g. missing files). In this case, you need to re-do the whole procedure.
Cache
When backing-up using hosting panels, we usually get the complete document root directory, that also includes the cache folder. However, you should not move cached files from another environment and it's possible that those may be the cause of the blank page you see. Open the cache folder of your local Joomla instance and delete everything from there - except of the index.html file.
Akeeba Backup
I would suggest you to use Akeeba Backup, follow their instructions on how to backup and restore, to do your task.
