Generally, when an update occurs, WordPress updates its main files and not the plugins / themes it is using. When only the main files are updated, the update is very likely to have an error - especially if you have made custom changes to your files.
If you updated not only the main files, but also custom modules / themes that you may be using, it could be the reason for the problem with the blank page. The solution is quite simple - disable all activated plugins. To do this (as you don't have access to your website's database), just run a few queries to your website's database. Please perform the following steps:
Step 1: Access phpMyAdmin through your cPanel -> phpMyAdmin;
Step 2: click on the name of the database your website is using (you can find it in the wp-config.php file);
Step 3: Run the following query:
UPDATE wp_options SET option_value = '' WHERE option_name = 'active_plugins';
This will disable ALL active plug-ins on your site without actually removing the physical folders.