Are you using Joomla 3 or 4?
Can you set the Error Reporting to 'Development' in the Joomla configuration and see what is breaking the page?

This suggests that it is trying to empty a folder, but it is taking too long. Maybe because the folder is write-protected or something.

Try emptying the cache folder manually (via FTP for instance).

You can safely delete all files and folders inside the cache folder. So you should end up with a completely empty cache folder.

So I guess it was filled with ages of old cache files 😬
That is very much down to how you use your website, how you have set up caching and how (and how often) you use Cache Cleaner in the administrator.

Personally I have it set up to clear the cache whenever I save an article. That and manually pressing the button when I need to, is enough.
I have no idea where VirtueMart stores its cache. If it is in the normal cache folder, then yes.
If it is in some other folder, you can set Cache Cleaner Pro up to empty that custom folder path too.
If it stores cache in the database, then you can set Cache Cleaner Pro up to empty that specific database table.