CentOS's Apache won't start

It is likely that you have a path defined in one of your configuration parameters that doesn't exist or has the wrong permissions. There are some that Apache will be able to start up with even if they don't exist, and others, like the main error log (there are others) that will cause it to fail to start. Look there.

Also, check to make sure it is not already running:

service httpd status

or

ps aux|grep httpd

If all your paths exist, have good permissions, apache is not already running and you see nothing in your syslog (/var/log/messages by default), then I'd start backtracking by removing the httpd rpm and re-install and start over.