A few guesses.
Do you have a master valve?
If so, you have a main line leak somewhere after the master valve but before the others. If it were after the zone valve then the other zones would work. Since none work and the red triangle spins rapidly while water barely trickles out then the break is before the zone valves.
That puddle at the end of zone 3 could be as simple as low head seepage or could be an indicator of where your leak is.
Since you manually turned them on with no improvement you eliminated the solenoids as potential problems.
I guess I should ask if you are in a free area and if your system was winterized. If so and the bleed screws are still open then trying to feed all 5 zones could result in the trickle you see.
Your system won't try to run two valves at once unless you wire it that way or the wires crossed somehow.