OK, this isn't really an answer but it's more than a comment. In your httpd.conf file make sure you have this line and that it is not commented out:
LoadModule php5_module modules/libphp5.so
That should be near the top of the file. Much further down you'll see some AddHandler lines. Make sure you have this:
AddHandler php5-script .php
You also might want to look to make sure this directive is in place. It gives Apache a clue for what file to try to serve if you navigate to a directory instead of a file:
<IfModule dir_module>
DirectoryIndex index.php
</IfModule>
Don't forget to restart Apache after changing your httpd.conf file.
For your installation specifically make sure you have the following files:
/etc/apache2/mods-enabled/php5.conf
/etc/apache2/mods-enabled/php5.load
When you were going through the steps of installing your LAMP stack did you do the test of creating the info.php file? I just created an Ubuntu 14.4 VM and followed all the steps and it worked for me the first time. Try going back through all those steps and double checking everything.