System call 53 is for TCP/IP connections. With syscall 53/5 you can open a tcp/ip connection in active mode to a remote computer and then use the returned socket number for all the following system calls. With syscall 53/6 you should wait for the connection to be established (state 4) and then use system calls 53/7,53/17,53/3,53/13 for sending and receiving data. Once the connection is over or closed by the remote computer, you need to close the connection with syscall 53/8. You can also open a listening connection with syscall 53/5 in passive mode for server purposes. See: http://menuetos.net/syscall.txt

Simply, you can't. You can't access Internet Card without use system calls, even you can, you need to implement sockets and other protocols again. This is job of the OS. This is purpose of the OS. Do not try to reinvent the wheel.