What NVR model do you have?
What camera models do you have? (both the working and offline cameras)
Roughly how long has the system been installed?
Were the cameras connected to the NVR with factory-made/pre-terminated cables or did you cut and terminate your own cables?
Ok, it looks like it is either a PoE port issue or a cable issue.
We would recommend taking that camera down and connecting to that port on a short, factory-made patch cable to test both the port and cable, if the lights come on and the camera powers up then it is likely a faulty cable and/or faulty RJ45 terminations, but if it also doesn't work on the factory-made cable then it is likely a faulty PoE port. You could try taking the NVR back to who you bought from for a warranty replacement, but if it has been installed for 3-years it will likely be out of warranty, if it is no longer covered then the workaround would be to connect the camera to a separate PoE injector that is connected to your router/LAN and then add the camera to your NVR over the local network rather than plugging it into the NVR directly. (that is if your NVR is actually connected to the network)
When you take it down - look inside the female RJ45 socket. If any moisture has got in, it will have caused a short. It'll be obvious as you'll be able to see the pins burnt/corroded.