First things first: without the IP address, you are likely out of luck simply because that machine's name is no longer registered in DNS - you can ping the hostname 'til the cows come home and never get a peep out of it. You'll need to scan the entire subnet for live IPs in order to find it. And if the random IP you set your workstation to just happens to be the same as your remote machine, you could have a whole bunch of trouble!
Secondly, depending on your router and any switches involved in your network, you may still not be able to reach the remote machine even after changing the IP address on your workstation to match. Many routers (and some intelligent switches) will drop packets if they are addressed to a subnet that is not configured on an interface for the router; this is a security feature.
Thirdly, even if an IP scan works, it could take a very long time. I'm not saying don't try it - but be aware that the time it takes to find and download a subnet scanner you like and then let it ping every address in the entire 172.18.2.0 subnet could take a while.
What I recommend that you do is pull the box out of the closet, hook it up to a monitor, and configure it to use DHCP (note the MAC address of your network card). Then set up a DHCP reservation for the remote computer on your router. Being on DHCP will ensure that this never happens again, and the reservation will give you essentially the same functionality as a static IP.