I am having trouble connecting to an Amazon Elastic Cloud Computer Instance via a browser. I attempted going to ********.compute-1.amazonaws.c
By default, your instances will only be in the default security group. If it's an EC2 instance you cannot change security groups while the instance is running, you'll have to specify them in advance. If it's a VPC instance you can change security groups at runtime.
default groupYou can however add the rule to allow port 80 to that default security group; just don't create a new security group as it can not be associated with the running instance.
Also, make sure that your web server is up and running. From your instance (using SSH shell access), check if the right process is listening on port 80, using the command netstat -lnp. You should then see a row with proto tcp and a Local Address ending in :80. The IP Address listed should be either 0.0.0.0 (meaning 'any IP') or a specific IP of a listening network interface.
If you are in need of a web server, take a look at Apache or Nginx. They both support PHP.
Hope this helps.