rubbish statement - takes two to tango
"No clue about VLANs, no clue about if it has STP, or trunking, or anything."
Yes you do - if you have access to the attached switches/devices to the core then you have the other half of the config. Totally agree with the previous comments on the mgmt side should ensure this situation doesn't happen, and backups (all things fail human and silicon) but as a network guy with 20yrs +, STP is a mutual thing as should be the vlan and trunking (packet sniffer will show up most of this). You will need down time for the replacement but hunt for the clues first on the wire and attached devices first if you really are situation. You should not get in to this situation and is bad working practise from all parties, it is a fire fight but not all is lost (if you do not know what your core switch is doing for your critical traffic with out seeing the config please find the door....oh you cant do that with out being provided a map I see your problem!)