How would I go about sending packets in the ICMP Protocol via Winsock Control? Or is this even possible.

you will notice that the Winsock control's "Protocol" property only supports UDP and TCP. ICMP is a much lower level protocol than TCP and is built primarily "into" the IP protocol.

Check http://www.faqs.org/rfcs/rfc792.html

Maybe you should look into the Winsock API. I don't know much about them, but they might help.