Oh, I just read your post again and have some valuable advice. I had this problem, and solved it. You could have salt clogging the jets beneath the rim. Back ream them with fencing wire. And there is a big jet at the bottom of the bowl that cakes up. That jet accelerates flush water into the siphon and if it's plugged (salted up) the toilet just fails to flush, with water in bowl slowly descending after flush attempt. You'd think there was something blocking the siphon; I've had that problem too, which required removal of bowl and inversion to dislodge obstacle.
Use a small pry bar, i.e., the right-angled head thereof, to break salt deposit from aforementioned big jet. I know you said "siphon jet not clogged" but I'm skeptical. How do you KNOW it's not clogged?
Meanwhile, if the tank won't empty, then you've got an obstruction in the bowl internals, up high. Right?