Try opening the dump valve, then go up on the roof with a hose, remove vent pipe cap and see if water will freely go down the pipe without backing up. Have a helper check to see water isn't backing up into the shower or sink and if it flows out the dump outlet pipe (may take a few seconds or more to come out) just in case.
There should be a one-way air admittance valve (AAV) under the sink which allows air to be drawn into the holding tank even *if* the roof vent is plugged. Check to see if the AAV is working and replace if needed. These do sometimes stop working.
The diagram below is a generic layout of the grey water piping that gives a basic idea of what the piping is like. (It's from Australia, ignore note on trap under shower as they are a requirement here and each sink & shower/tub must have it's own P-trap here). You can see that a plugged roof vent would still allow the tank contents to drain, although maybe slower. If the roof vent is plugged, water draining into the tank would tend to pressurize it and cause water to back up into the sink or shower. P-traps that will be under the sink & shower are there to prevent tank odors from directly venting inside and aren't affected by water flow direction but could be sucked dry if an AAV isn't working.
It does sound like the vent pipe has dropped. If you remove the vent cover on the roof, you should be able to see the ABS at roof level. The pipe could have an offset between the roof and tank though. Sometimes you may find the pipe accessible in a closet or cupboard (like in ours). Providing you can draw the pipe back up to roof level where it should be, try and find a spot somewhere between roof and floor level where you can use a clamp or strap to secure it.