Have never seen this on a range connector but here is the problem as you described it.
The transformer that feeds your house has a secondary that is 240 volt center tapped.
There are 3 wires between pole and house/apartment. (NOTE: Pole may be underground and so may the wires)
L-1, Neutral, L-2
The "Neutral" is the center tap of the transformer and is also bonded to ground at the pole.
Now.. Proper wiring for a Range, or Dryer or 240 volt appliance or 50 amp RV outlet (All are wired the same) is as follows. (Periods are space holders)
. Neutral
L 1 - - L 2
. Ground
NOTE that L 1 and L 2 are arbitrary and may be reversed safely In fact it does not matter if they are reversed.
Now, here is how yours is wired
. Neutral
L N - - L N
. Ground
N, means it's the same leg, both sides.. This is simply wrong and will not work.
NOTE: there is an option 2.... ALas, you eliminated it.
Generally all the indicators, lights, clock etc run off one leg.
IF the OTHER leg has a very high resistance, the elements will not get hot.. But you would also not see zero volts side to side.
So make sure your side to side measurements are in fact side to side and not neutral to ground (Which should be zero)
Ground is USUALLY the "Different" pin (L Shaped, U-Shaped whatever)
