You can't use ICMP alone to discover if a service is up. It's just another protocol that the machine happens to accept and have appropriate daemons for. A ping will show you that the machine is up and accepting ICMP ECHO requests, but it can't tell you that a service is listening on a TCP port. Since some servers don't respond to ICMP requests or have firewalls that block those requests, ICMP won't always be reliable.
In order to test if a specific service is up, just attempt a TCP connection to that service.
In order to test if your route to the host is being blocked, use a VPN and attempt to access the site from a different country. You could also use a down/up test like http://downforeveryoneorjustme.com/ to test if the HTTP daemon is up and available from somewhere else.