This is a really odd request. How can a device have an unknown IP address? And it has no software? Whoa...

But I would log on to a box on the same subnet as this mystery box and ping the broadcast address. It should respond. If it is talking to the outside world (beyond the local subnet) it is talking via a router that must know its IP/MAC address pair. Dumping the arp tables on the routers should do it.

Another thought... unplug it from the network. If anyone complains about a box that went down contact them for more info. If this box is not in DNS how do folks access it? It may not be in use at all.