I suspect that "unable to access the Internet" means unable to download other web pages. The Internet !=
WWW.
If you configure a proxy in the Network Prefs then Safari will use that proxy for
all HTTP web pages. If the proxy used to access the database only provides access to the database, and doesn't allow general WWW access, this would explain your problem.
If, using the proxy, you are able to access the database you can do one of two things. Either uncheck the proxy settings and apply them when you want to access other sites, or set up a different Location in Network prefs that includes the proxy settings.