The system ping typically is suid-root

$ ls -l `which ping`
-rwsr-xr-x 1 root root 40048 Dec  3  2008 /bin/ping
   ^         ^
[download]

which is why it does work (using 'icmp' method), while your unprivileged script does not.  I don't think you're going to have much luck running this unprivileged.