The problem is if you send it as BROADCAST it will be send to all client but not to your self. (Read the manual)

How about adding another Event send function just to yourself?

Code:
function chat_startup()
{
	// everything as it was
	
	while(1)
	{
		if(key_c == ON && enet_get_connection() != SERVER_MODE)
		{			
			enet_clsend_event(17,tmpMsg,0,BROADCAST); //sends the chat msg to everyone
			
			if(enet_get_connection() == CLIENT_SERVER_MODE)
			{
				enet_clsend_event(17,tmpMsg,0,enet_get_clientid()); //sends the chat msg to me
			}
		}
		wait(1);
	}
}