rut,
You might want to ask this question in the Chinese tractor section to see what other Jinma owners come up with.
If you haven't done so already, since you have a new battery, is take the ground from the battery off the frame. Then use an angle grinder to remove any paint or rust from the frame down to bare metal. I used a star washer to reconnect so it "bit" into the metal for a super good connection. Check voltage of the "new" battery too. Sometimes the connection will be good enough to get the starter to crank, but if it's not perfect, it will start to oxidize and you'll lose current as there is more resistance from the poor connection.
You'd be surprised how many electrical problems stem from a poor ground, even if it looks good. Try that first and go from there.
You can use your decompression lever to let it turn over easier, but it sounds to me like a bad connection.