Using the browser I just enter 192.168.2.1 (or whatever it may be) to get to the login page.
To access the start page you do not need to enter any file name.
The well-known Arduino Ethernet example shows the usage:
Serial.println(client.remoteIP()); // Make a HTTP request: client.println("GET /search?q=arduino HTTP/1.1"); client.println("Host: www.google.com");
Of course I know I have to replace the host name.
But whatever I insert between GET and HTTP (even * and ?) the Arduino does not get any bytes as response.