Look at the pics I posted in #8 that "tab" is what the run/stop solenoid pushes on to stop the engine, it looks like it is in the stop position, see if you can gently get that "tab" closer to the throttle shaft, should almost be touching and see if that spring gets uncompressed.
EDIT, that tab pushes against the run/stop solenoid, all the run/stop solenoid does is push it into the stop position, it is up to that linkage to go into the run position when the solenoid stops pushing on it, it is spring loaded and is not "pulled" into the run position by the solenoid.