The switch MAC database is the best way to do non-intrusively, but since you say you can't get there, you're going to have to tear things apart.
Start pulling the network apart, piece by piece and, as you do that, attempt to PING the device between changes. Disconnect Ethernet switches until you can make the offending host stop answering. (If it doesn't respond to PING, clear your ARP cache and attempt to PING it. It'll probably answer for ARP even if it doesn't answer for PING.)
Once you narrow it down to a given switch, I'd recommend doing a binary search to pinpoint it as quickly as possible (disconnect half the cables, see if it's there, disconnect half of the half where it was located, repeate until you locate the offending device).
What's the MAC address, if you don't mind me asking?