Public hosts for ping
Solution 1:
I'd recommend avoiding ping and looking at something like curl or telnet. You need to do this in two parts though, because it could be a nameserver issue.
Step 1: Verify functioning nameserver
Step 2: use curl, wget, or telnet (on port 80) and search the results for any known text.
This is better than pinging since you pretty much KNOW Google is going to be around to serve your requests on port 80.
Come to think of it, you could just do an nslookup on one of Google's nameservers (8.8.4.4 or 8.8.8.8) and if that succeeds, you're good.