Okay, here is a totally hillbilly (no offense to hillbillies) idea using things you might have around the house. Duct tape a flashlight and iPhone or digital small camera to a slinky. Turn on the flashlight and turn on the video recorder. Push it down into the vent as far as it will go. When you pull it up, check the video to see if you can actually see the ring in the vent.
Or skip the camera and flashlight, and put a wad of duct tape on the slinky (or just some kind of rope) and maybe the ring will stick to it? Good luck! I think plumbers have small flexible cameras that can see into even small pipes. That would be an expensive house call, but it could be an option if the landlord can't help you.
ETA: Disregard my suggestion. I didn't realize it was a vertical drop. I thought it just angled downward and was a long distance from the actual vent. You should just stick with calling the landlord :-)