There’s tools like Angry Scanner that will ping all the IPs in a range. Find the one with the MAC address of your device, and ta-da.
The first 6 hex digits of the 12-digit MAC address are the manufacturer code. Google ethernet manufacturer codes and see if the suspected MAC code matches who made you box. If you can’t plug the device into a tame network first to determine the MAC address (as mentioned above) then if it’s only one of a few such devices on the network, you can try all of them. Most devices list the MAC somewhere on the box.
Or let’s say you think you know the address but want to be sure. Then ping the address continuous, i.e. in a DOS command box run command > PING aa.bb.cc.dd -t (where aa.bb.cc.dd is the address). The device will ping continuously. Unplug the network, ping should time out. Plug back in and it resumes.