ethernet shield+apache+php: client connect fails

If the server is a domain name, and not an ip, then you should send a "Host" in the header. I see you sent "Connection: close", so that normally infers HTTP/1.1. Note the change in the GET send.

    client.println("GET /myFile.php HTTP/1.1");
    client.println("Host: www.mydomain.com");    
    client.println("User-Agent: Arduino"); 
    client.println("Accept: text/html");
    client.println("Connection: close");
    client.println();