1. Ping to external IP address proves connectivity only.
2. Ping to external FQDN proves both, connectivity and name resolution.
3. However when ping response is not allowed on target external computer, you should another external server (preferably this one that can be pinged by another computer).
4. Check security settings on your server and make sure that there is no barrier for MS update servers. Make sure that the same is true when acessing other secure web pages (https).
5. FTP is another story, wht you should do depends on the type of FTP(S) server (passive, active, secure,...)
6. Hope your workstations DNS settings points to local server DNS only and not to public one.
7. Hope you have not multihomed server.
8. What DNS configuration do you have in server to resolve external servers (forwarders,...)?
9. Share log files from Wireshark if you feel like not to analyze them, share ipconfig on workstations and server, try to analyze healths of DC with respect to DNS,....
HTH
Milos