You've been reading a very old thread and the suggestion concerning deflate being the culprit, might be true, but have had no issues similar.
Since you've transferred the site to a Linux server, was the old site Windows? If former server was Windows, did you use the moodle code from Windows or install fresh Moodle code (matching version) from the .tar.gz files. Copying over your config.php file, of course.
In your httpd.conf find this line:
LoadModule deflate_module modules/mod_deflate.so
and comment it out. Put a # character in front.
Check your .htaccess file if you have one for re-write rules related to PDF files.
From /var/www/html/ as root user:
fgrep '.pdf' .htaccess
You may NOT have an .htaccess file and that's ok.
Restart your apache server: /sbin/service httpd restart
Check error logs: tail /var/log/httpd/error_log
For any errors on restart. Try your PDF links.
And a comment about your config ...
Set ServerSignature to off
No sense in giving more information than is needed on 404's.
Also, at the very bottom comment out all the settings you've opened for virtual servers. Doesn't really appear you are running virtuals and they are not needed since you are running moodle from /var/www/html/
Add a # in front of:
Document root is already defined and one doesn't need ServerName to be an IP address. If your firewall allows port 80 Apache (httpd) will respond to any request of a browser to the server's IP address.
'spriit of sharing', Ken