Have you tried connecting the camera directly to your laptop / computer (powered through PoE Injector)? You can always draw the IP from there and be able to hopefully login and set a static IP.
I spent the weekend trying to figure this out, but have pretty much given up. I have it isolated to an issue between the switch and the camera. I have the camera hooked to a PoE injector for power (to eliminate power as a factor). When I plug it into the Unifi 8-150 it shows up in the unifi network with a MAC address only but does not get an IP (if static still gets no IP). Cannot ping it (static or DHCP). Tried multiple ports on the switch.
If I then plug the camera into a 25 port unmanaged switch fed from the 8-150, the camera works great.
I then tried the same test, but used a old 4 port 10/100 switch fed from the 8-150 Unifi switch. It did not work. Same affect as plugging the camera directly to the Unifi switch.
So, no clue at this point. I'm thinking some hardware, software issue in the camera that is a timing or handshake error that is on the edge of working/not-working.
Not worth the aggragvation - will purchase a new PoE switch to use for the cameras and test that out. Just lose the ability to manage the switch from Unifi.