Where can I find messages related to Apache start up?

You could go to a terminal and type in "sudo /etc/init.d/apache2 restart" in a terminal, and see what kind of error message you get. One common reason, I believe, is because of some module that was either added, changed, or had a change made to a corresponding config file (such as php.ini). If all else fails, go to the directory /etc/apache2/mods-enabled, and move module links out into a temporary directory, and if apache starts, you can put them back one by one.

Be aware, though, that the error message may be misleading. It may get an error loading a module not because the module is bad, but because it's configuration file is bad.

from:

View log files in Ubuntu Linux
http://www.cyberciti.biz/faq/ubuntu-linux-gnome-system-log-viewer/

/var/log/apache2/*  :  Apache web server log files directory

Typically you will get a message like this:

Job for apache2.service failed because the control process exited with error code.
See "systemctl status apache2.service" and "journalctl -xe" for details.

So all you need to do is run:

journalctl -xe

Then you should see an output similar to this

Nov 16 03:27:26 naboo sudo[9909]: pam_unix(sudo:session): session opened f
Nov 16 03:27:28 naboo systemd[1]: Starting The Apache HTTP Server...
-- Subject: Unit apache2.service has begun start-up
-- Defined-By: systemd
-- Support: http://www.ubuntu.com/support
-- 
-- Unit apache2.service has begun starting up.
Nov 16 03:27:29 naboo apachectl[9939]: (98)Address already in use: AH00072
Nov 16 03:27:29 naboo apachectl[9939]: no listening sockets available, shu
Nov 16 03:27:29 naboo apachectl[9939]: AH00015: Unable to open logs
Nov 16 03:27:29 naboo apachectl[9939]: Action 'start' failed.
Nov 16 03:27:29 naboo apachectl[9939]: The Apache error log may have more 
Nov 16 03:27:29 naboo systemd[1]: apache2.service: Control process exited,
Nov 16 03:27:29 naboo systemd[1]: apache2.service: Failed with result 'exi
Nov 16 03:27:29 naboo systemd[1]: Failed to start The Apache HTTP Server.
-- Subject: Unit apache2.service has failed
-- Defined-By: systemd
-- Support: http://www.ubuntu.com/support
-- 
-- Unit apache2.service has failed.
-- 
-- The result is RESULT.
Nov 16 03:27:29 naboo sudo[9909]: pam_unix(sudo:session): session closed f