Strange stalling problem

I am having a problem with my car. I started my car with heaps of juice in the battery, reversed a bit and the car stalled, quite strange. I restarted it again with great cranking drove about 400 meters and it stalled suddenly again. Like it had ran out of fuel, (which is actually LP gas as its never run on petrol). It had enough gas in it though. So l restarted again with heaps of crank and it fired up again. Drove 50 meters and it stalled again. Now here is the weird part. L went to restart the car and just click click. Lights on the dash were on and l could hear the solenoid clicking but no crank at all. What l cannot understand is it stalling, but now suddenly now crank whatsoever. L charged the battery just in case, but no go. Tried a new battery and still click click click. I am hoping someone out there has an idea on what is going on with it as it does not make sense to me. I have unfortunately ran out of gas before and the stalling this time around feels and sounds exactly the same, but then why no cranking? Please help someone.