Just to check whether or not it's a standard file permissions problem: if you can access a shell, cd to the directory which holds your wiki and change the owner of all files and dirs to apache:
cd /var/www/html
chown -R apache dokuwiki
If this doesn't help, check to see if selinux is enabled. I remember having a similar problem once because of selinux. At the command line:
sestatus
If it is, google for ways to disable it. Or to set it to permissive mode. It may be enough to change the config file in /etc/selinux. But I'm not reallly qualified to advise on this.