A model number may help others help you.

Most GE's fill to just under the heating element.

One way to check for a low fill is to add a couple quarts of hot water after each fill during a cycle. If it now washes OK then low fill is the probable problem.
Just be careful to not overfill it.
Also often a low fill will result in a growling noise from the pump as it is sucking in air.

If it is low fill then turn off then water supply to the unit.
Place a shallow pan under the fill valve (usually under the unit, behind the kick plate on the left hand side).
Remove the valve from the unit and check the screen filter built into it's input side.
If dirty clean it.
Do not permanently remove it, as it is there to keep crud out of the valve which could hold it open and cause a flood.
If it is clean I would replace it.

If it is not low fill then remove the sump cover.
Check in the sump for debris or something wrapped around the chopper.
Be careful as there is often broken class in the sump.
If the unit has it check/clean the filter at the back/bottom of the tub.

I cannot find any info on your unit.
If this is a non-USA unit then I will not be able to get any info for you.

Also I do not understand the rest of your post.

Since it is a Canadian model I will not be able to find specific info on it.

A common cause for no or low fill is a partially plugged screen filter.
There is a screen filter built into the input side of the water valve.
The valve is usually behind the kick plate under the unit on the left hand side.
Shut the water supply off and remove the valve, then check/clean this filter.

Do not permanently remove it as it is there to keep crud out of the valve which could hold it open and cause a flood.

[COLOR="DarkRed"]Some cycles will fill OK.. others will not.[/COLOR]
This concerns me as it could be the timer though the water valve would still be at the top of my list.
If this is reliable, in other words it always runs OK in one cycle type and always fails in another then it points more towards a timer.
If the unit has soil sensing then that may be the problem. You would have to determine on what cycles is soil sensing is used.

If a cycle type runs OK and then the same cycle fails the next time then the problem is intermittent and the filter screen may be clean but the valve itself is not opening reliably.

The solenoid will stay in the drain position (down) until the unit is empty.

The way it works is when a drain is called for the timer powers the solenoid for a few seconds. The plunger is pulled down into the drain position, this then moves the wash/drain flapper to the drain position. The water pressure then holds the flapper and plunger in the drain position until the unit is empty and then the springs pull the plunger back up into the wash position.

I would monitor the power to the solenoid. If it is powered longer that a couple seconds when it fails it is a timer problem.

If it is powered correctly, with the unit off manually actuate the solenoid to see if it is OK mechanically.
If it sticks I would remove the solenoid and check that the plunger is free.

What can happen sometimes is that the solenoid can be powered for too long, this causes it to overheat and the plastic in it melts/deforms and can cause the solenoid to stick. If this is the case then the timer and solenoid should be replaced.

Remove the spray arm from inside the tub so that you can see the flapper valve and inspect it.

I cannot say as I do not know which type you have.
Some have a locking tab, some just unscrew (left hand thread, I think).

The following may help.
http://www.applianceaid.com/dishwash.html