The combined steps are correct between the question and the comments. You just need to debug every step.
Google "DNS lookup", I usually use www.dnsstuff.com, but choose what you like. First check that the name servers are the ones you entered with your case; if not, double check that you told your case to use them, otherwise just wait longer. If so, double-check them for the values in the Route 53 panel.
Then check the value of the A record registered against the one you entered. Make sure that you select “simple” as the route policy of route 53 and set “Alias” to “No”.
If the above two values are correct, make sure your Apache server responds to port 80 and browse to the IP address of your server in the browser. If this works, one of the two steps above is incorrect (and make sure it is not someone else installed by Apache), or it has not yet been distributed. If this does not work, make sure that the security group set against these instances resolves all IP addresses on port 80 (i.e., 0.0.0.0/0).
Pay attention to the security group administrator’s interface after you add the rule, you still have to “apply the rule change” before it takes effect.
If you allow the inbound configuration of the security group, it still does not work, you either do not have the correct Apache on port 80, or you have something like iptables that uses the internal firewall on the server. Try something like www.yougetsignal.com using the IP address and port 80. If this works, the problem is most likely with Apache.
If you have problems at this last step, run the Linux background image, just install Apache, use the same security group and verify that the Apache instance responds using the public DNS Amazon of that instance through the browser. If this works, but you still don’t, you did something normal for your instance that only you can debug.
If everything is correctly specified in the remote DNS lookup reports, but not locally on your computer, clear the local DNS cache and try again.