Security Groups and Security Rules in AWS. (63 of 285 technotes for 2015)

• Security Group - acts as a virtual firewall that controls traffic for one or more instances.
  
• You can add multiple Security Groups to a instance.
• You can add multiple Rules to a Security Group.
• The rules from different security groups and aggregated and applied to the instance.

Caution:

Because you can assign multiple rules to a security group, an instance can have hundreds of rules that apply. This can cause complexity. 

Suggestion:

Condense your rules as much as possible,

Cannot ping a Elastic IP Address in AWS. (59 of 285 technotes for 2015)

Check the Security Group associated to the instance. Most likely the incoming rule for ICMP Echo Request is disabled.