This is actually quite a simple fix. I downloaded GameMaker Studio and began messing around. I quickly noticed that GameMaker Studio does not understand escaped characters. You must instead use the chr function to send CR and LF through the socket:
var buff = buffer_create(1024, buffer_grow, 1);
buffer_write(buff, buffer_string, "NICK justinfan423452345"+chr(13)+chr(10));
network_send_raw(irc_socket, buff, buffer_get_size(buff));
buffer_delete(buff);
Character 13 in base 10 is ASCII for carriage return (CR), and character 10 in base 10 is ASCII for line feed (LF).