This issue is almost identical in symptoms to a ticket posted last August:-
https://www.akeebabackup.com/support/akeeba-backup-3x/17041-configuration-wizard-failure-and-backup-failed.html
It's not clear from that thread how the OP's issues were resolved. Plus, the difference between that and our circumstances is that our cPanel log doesn't report errors for non-existant Akeeba plugins.
Problem description
Any attempt to run the configuration wizard yields:-
Configuration Wizard Failure
Akeeba Backup could not find a writable output and temporary directory. Please give write permissions to the administrator/components/com_akeeba/backup directory and run this wizard again.
Manual configuration appears to work just fine.
Any attempt to run a backup yields:-
AJAX Loading Error
HTTP Status: 403 (Forbidden)
Internal status: error
XHR ReadyState: 4
Raw server response:
Forbidden
The 'percentage done' varies from attempt to attempt, suggesting a timing/server load issue rather than anything with the file system.
Diagnostics performed - filesystem
I coded a PHP script that writes a test file to the administrator/components/com_akeeba/backup directory. I can confirm that this succeeded.
I coded another PHP script that recurses through the entire file system, and flags up messages for any file that has permissions other than 644, or any directory that has permissions other than 755. I confirm that no directories were flagged up (and the script was tested by manually altering a directory picked at random). A small number of files were flagged up; I can list these if required.
As yet I've not completed an exhaustive analysis of .htaccess. I'm not an expert in the format of this file, so this area of fault-finding is on-going.
Disk space usage is currently just under 95Mb of 75Gb. I have purposely uploaded (via the cPanel file manager) approx 40Mb of test files, and I can confirm that these file were correct when downloaded again via HTTP URLs.
Other than any .htaccess weirdness, I don't have any explanation as to why the configuration wizard would object to not having a writeable output and temporary directory.
Diagnostics performed - timing
I coded a PHP script with a couple of nested for () constructs to create a tight loop of CPU time wasting.
I can confirm that via set_time_limit() I can easily run for 60 seconds or more. No apparent Zen server constraints interfering with heavy script load.
I have manually experimented with the execution-related config options as discussed here:-
https://www.akeebabackup.com/support/akeeba-backup-3x/14800-configuration-wizard-failurefailed-backup.html
to no avail. Backups still fail.
One last clue?
As a test I did change the backup type to 'database only'. This consistently works, and only when I change back to 'full backup' do backups then consistently fail.
This could be symptomatic of either a file system issue or a timing issue of course.
I'm currently out of ideas. Suggestions welcome.