Ethernet client connect with password?

If that is the correct base64 encoding of your user:password, then:

 if (client.connect(server,80)) {
    Serial.println("connected");
     // Make a HTTP request:
    client.println("GET /search?q=arduino HTTP/1.1");
    client.println("Authorization: Basic QzF5WXIxXG15cW14FkJheWVyMTIz"); 
    client.println("Host: www.google.com");
    client.println("Connection: Close");
    client.println();