Faulty/dirty/corroded internal ignition switch contacts? Same for neutral safety switch contacts?
(does the VX have an actual neutral safety switch aside from the transmission mode selector switch which is often called 'neutral safety switch'?)
When you say "first try, nothing" do you mean the engine starter does not even try to turn? No sounds whatsoever?
On "Second try: turns once" do you mean you can hear the starter engage and try to turn the engine but the engine doesn't fire? Or does the engine fire once for a revolution or so then not continue to run?