Okay, what you did helps to clarify the reason of the blank page, the core integrity checks works in two steps, the first one is a communication opened between your site and one of the public WordPress API services, the plugin uses this to retrieve the checksums of every core file part of the archive released under the same version number installed in your site.
The second step involves a file system scan in your project in the root, includes, and admin directories. Then the plugin compares the checksum of the files found during the scan with the data retrieved from WordPress, depending on the matches the plugin displays a warning with a list of files that seem to be affected by an addition, modification, or removal of WordPress core files.
Following this, we can assume two possible issues. One is that the server where your website is being hosted is/was not able to communicate with the public WordPress API. The second option is that there are too many folders/files in your project and the PHP interpreter could not sustain so much data in the memory allowed by your hosting provider, the server forces the interpreter to kill the script which translate to a failure in the load of the page, in this case the dashboard.
The “Core Integrity Checks” is one of those features that do not make sense to deactivate, but some features in the plugin depend on external resources that can not be controlled from the code.
I will think of a solution and update this thread when I have an idea.