To OP,
Since you have not provided any schematic of the control board it would be hard to come up with a convincing response that is based on actual installation.
All you can expect is a lot of conjectures, guesses and assumptions.
Here is a generic engineering setup. Depending on the needs of the customer or sophistication of the wiring scheme, this diagram could employ several features. A lot of variance may be employed but the principle stays the same.
In the diagram it uses four gated transistors to drive LEDs. These LEDs could be substituted with a direct load to drive a small solid state relay for instance.
Instead of using simple transistor (SL100) whose gates are triggered by each dedicated probe, you can substitute an IC solid state that could employ an anti-cycling feature to prevent the pump from short cycling. These are all mounted in a PC board. Yes, there is a PC board. This is available online.
You may not think that there's logic circuit because only the ice cubes are visible. If you notice, there is a hockey-pock-looking disc mounted on the side and there is no conventional laminated core transformer on the board itself. This hockey pock is an encapsulated toroidal transformer as opposed to the laminated "E" core old-school transformer. It has small footprint.
This criteria does have in its algorithm. . . the ability that, in case there is an event that will lead to short cycling (dirty probe, liquid turbulence, etc.) it initiates a lock up feature after pump failure .
Pump failure would cause flooding and thereby causing all probes to be submerged. This could also happen during power failure.
The control design engineer (I have designed a few) didn't want the pump to restart automatically after restoration of power. In this type of PC board, a combination electro-mechanical latching relay is required as opposed to all-electric pump motor failure safety feature. (which is probably what you have)
This scheme is evident when you claim that you have to recycle (or reset) power by turning it off and on.
It requires human intervention to prevent further damage especially when control and motor are still submerged in case the motor is non-submersible.
Not ignoring others' inferences, it sounds absurd to think that the system is wired wrong. . .for the simple reason that it was working before.
My comments are based on the graphics you've presented. . . feel free to disambiguate.
http://2.bp.blogspot.com/-464IgyinGWM/ViCQ24xhkbI/AAAAAAAAALM/L5C3t5S4YnU/s1600/water%2Blevel%2Bindicator.png