Fine. Now we know that there is one miscreant amongst a bunch of solid citizens. Assuming that the 6360 is connected into the LAN at startup, do you have three solid LEDs (of four) or one solid LED (of two), or is the LI (link) LED blinking madly? If so, connection (autonegotiation) is not being achieved with the switch. Dud card, dud cable, or dud switch (which you can obviously rule out). A 10/100 card (usually, but not always, with four LEDs) almost certainly can autonegotiate with the switch if the 'physical layer' from card to switch inclusive is intact.
If the card is not being 'seen' it is not going to talk to anyone, either. It could again be a dud card, or it could lack critical software. My first guess is that OT is not installed. Single-click AppleTalk in Control Panels and do a command-i interrogation on it. If the Get Info. window does not show 'Apple Talk/Open Transport 1.1.2', you have found the problem.
OT 1.1.1 and 1.1.2 have to be installed manually, or once a year, up until OS 8.0 or so. Inevitably, other components of OT will also be missing, but Network Extension 7.6 should be present. AppleShare
3.8.3 is also a wise addition.
If this doesn't allow you to configure the card, you will have to suspect some deep-seated malaise justifying its replacement. You are certain that it is an Apple card? If so, it should be plug-'n'-play, but if it is an Asanté, Farallon, Dayna and so on in Apple's clothing, you will have to identify it and get the drivers before you can finally decide that it does or doesn't work.
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