Thank you for the reply. I chose "UDP" because it is the Net::Ping's default. "TCP" likewise returns unreachable.
If I change it to 'icmp', it DOES work, but only if effective uid is root (per the module's documentation). I wanted to run this w/o root privs, just as a plain user.
There are indeed other services available on this server, but I don't see in the Net::Ping documentation any way to specify a different port number from the default ('echo'). Perhaps the only thing I can do is run it as root or setuid the script. But any other advice would be helpful.