It feels like the handle doesn't move at all the valve may be stuck. If it's not frozen and it is moving free (resistance is ok fine) then your tank is likely clogged in the worst possible condition.
This will allow you to safely troubleshoot. Throw that on (close it) then open the original. You can then move on to recommendation #2 and that is a drain snake from the topside to get past the gate valve hopefully. If you are clogged then you have to physically break it up. They make all sorts of flushing things from the outside, or the inside but if it's really clogged and full then it's back to basics. Lots of tricks with hot water blah blah but sometimes you are in a bad spot. You can also consider getting a septic service to pump you out if you can't get it.
I created an adapter that allowed me to run a snake from the drain pipe side, with a cap on the end to prevent exfil. That didn't work. I went to a spot where I could hook it up and work on it with the pipe open and a clear adapter. One guy watching while I ran a power snake and then viola.
Then, I filled a 5 gallon bucket with water and dumped it into the toilet again and again and again while my observer commented on size, color, speed of exfil lol.
What a chore. This was all due to the previous owner not taking care of business so to speak.
The wetter you keep your tank the better so then when you are driving down the road it sort of agitates itself. Another trick is dump a bunch of ice in before driving. That is supposed to sort of scour then melt. Anyway none of that is going to help you with the current issue.
Anyway good luck soldier. PM me if I can help, what an odd thing to be an expert in huh