WINSOCK - Setting a timeout for a connection attempt on a non existing IP?

I am developing a RTSP Source filter in C++, and I am using WINSOCK 2.0 - blocking socket.

When I create a blocking socket, I set its SO_RCVTIMEO to 3 secs like so:

int ReceiveTimeout = 3000; 
int e = setsockopt(Socket, SOL_SOCKET, SO_RCVTIMEO, (char*)&ReceiveTimeout, sizeof(int));

My filter tries to connect to IP_ADDRESS:554 (554 is RTSP server port). If there is a server listening on that IP on the port 554, all goes well, but:

1. If my filter creates a socket to an existing IP address, but on a random port which no one listens on, connect() waits for 3 secs and returns WSAETIMEDOUT. So after 3 secs, I know that the provided URL is bad.

2. If my filter creates a socket to a non existing IP address, and tries to connect it, it hangs for about 10 secs before returning SOCKET_ERROR. So, SO_RCVTIMEO gets ignored if the IP doesn't exist on the network...

QUESTION: How can I set the timeout for a non existing IP, in the second case? Do I need to send ICMP PING first to see does the IP exist, or perform some other check like that?

Any help will be appreciated. Thanx. :)

THE ANSWER TO MY PROBLEM

Because I am using blocking sockets, call to connect() blocks, until the connection is made, or the connection fails because the host is not responding, or it is refusing connection. If I set socket's timeout to be 3 seconds, and try to connect to a host that doesn't exist, my pc (client) will send TCP packet with SYN flag set, to initiate the Threeway handshake. Normally, the host, if up, will respond with TCP packet containing ACK and SYN flags set, and then, client (me) would send the TCP packet with ACK flag set. Then the connection is made. BUT if the host is do