We're not psychics; all we can tell from the information you've provided so far is that your network allows pings (ICMP ECHO requests and responses). Your delay with nslookup might be due to misconfigured reverse DNS per FAQ 8.22. Then again, it might not.
If you want help from us, you'll have to provide more information. Examples:
- The contents of /etc/resolv.conf
- The output of $ route -n show -inet
- An ascii "graphic" of your local network configuration if applicable
- Your PF firewall configuration if applicable
Be sure to redact any private IP addresses / DNS names.