I enabled Web Proxy and used the same proxy settings as for Internet Explorer. I triple-checked the server address, port, username and password. In spite of that, using any menu commands that require internet access logs an error message that contains "Proxy requires authentication (QT code 105, HTTP code 407)".
I even tried disabling Web Proxy, it logs error messages containing "Connection timed out (QT code 99, HTTP code None)".
The only command not affected by this is "Lookup in Browser", which works regardless of the Web Proxy setting. At first I suspected firewall settings, but Picard works when I switch from LAN connection to 3G, and disable Web Proxy.