What I see on the screenshot is different to my installations. In the header, the term "MODX revolution" before the version number is missing. Maybe it's a different language version, but I guess not.
Besides that, I can't see anything odd in the phpinfo. Yes, php running as apache module instead of fast CGI. That might bring strange behavoir with it. Is it your own server and would you be able to change it into fastCGI Webspace? That would make the scripts run under different permissions.
There are several logs you might have to look into. First of all: MODX log. It's a shame, but its located in the core/cache folder. Do you still have it or did you delete it trying to refresh the cache?
If you still have it: open it, refresh the tab with the non working manager and open the log again. Compare.
The second log is the php log. In your case it's the apache log. Depending on the Linux your server runs at it can be located in different places mine is at /var/log/apache2
Do the same to this log as to the MODX log (if you can access it).
Good hunting!
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