What prevents a machine from responding to pings?

I dont' think that it's related to ping problem, but if you want to put selinux temporary off, you have this option:

setenforce 0

it put selinux from enforcing to permissive mode, to check its condition run

sestatus

to diable selinux permanently you can use system-config-securitylevel or edit with nano or vi /etc/selinux/config and change the parameter from SELINUX=enforcing to SELINUX=disabled.

for me there is a rule in Amazon EC2 that prevent to allow the ping traffic between your machines...