Special thanks to the user on this forum catservants, who discovered
that proxies may interfere with Apple only applications from gaining internet access. You might find that Netscape and Internet Explorer work, while Safari, Mail, and Software Update do not. If this is the case, one solution is to turn off the proxies.
1. Go to Apple menu -> System preferences -> Network.
2. Select the active port which is green, and click on Configure.
3. Go into Proxies, and uncheck all the proxies.
If that enables the internet connection in Safari in the Applications folder of the hard disk, or Software Update from the Apple menu, you may finally find internet access for other Apple applications work.