Hi
Well, although ping is an universal connectivity tool, really useful, ping fail does not mean something is broken on your network. A feel condition may cause the ping to fail like ACL and Firewall.
As you said all service is running fine, you probably have some ICMP limitation into your network for some reason. As I said, ping is good to have but is not a requirements for thing to work.
-If I helped you somehow, please, rate it as useful.-
