Despite dealing with the (bad) tonsillitis, today (especially towards the end) proved to be productive. On tonight’s menu : dead domain controller demotion, plus checking Service Principal Names duplicate entries. That made me discover a lovely little utility included in windows : LDP.exe
Removing the SPN entry drove our Sharepoint blind, couldn’t see the database server anymore! That’s certainly linked to Kerberos. I’ve added again the SPN entry in ADSIEdit.msc and all is fine again.