You can't ping the EC2 instance because by default the security group assigned to your EC2 instance will be blocking ping. To unblock it, modify your security group and add a Custom ICMP Rule to allow Echo Request and Echo Reply.
As for getting your DNS to work within IIS, if I were you to start with, I'd remove all bindings from IIS and then see if you get anything when using your subdomain.
Double check that your subdomain definitely resolves to your elastic IP, you can do this through a command prompt, e.g. nslookup subdomain.domain.com