If an HP DL360G6 (and likely other HP stuff as well) forgets who it is in ILO - including blank serial number, blank product ID, and all-zeroes “UUID” (the dash format is correct but it’s not a proper UUID) you should immediately suspect a dead (or missing!) bios battery. The battery type, somehow hard to google, is a CR2032 in this case.
On the DL360 this battery lives under the plastic RAM and CPU cover, near where the torx wrench is stored. There is a line diagram of the layout on the underside of the system cover (also includes the handy password bypass switch for the ILO).
Screenshot of the ailing HP: