ice maker water line leaking out the back of unit

So, our ice maker stopped making ice completely.

1st inspection showed ice build up around the fill cup. Figuring that just built up over time, I defrosted fill cup and put everything back together.

No ice.

2nd inspection showed a LITTLE ice build up around the fill cup and the fill cycle all leaking out the back of the freezer at the fitting where the hose connects to the fill cup chute. So I removed the ice maker and also the panel behind it which revealed SIGNIFICANT build up of ice around the freezer’s fooling fins. I defrosted all of that, put everything back together and the fill cycle still all leaks out the back fitting. It also has a near continuous SLOW leak during the time between fill cycles.

What are my next steps?

A model number would be useful.
http://www.appliancepartspros.com/modelnumber_locator.aspx

The slow leak is probably due to the water valve. I would replace it.

Then you may need a new fill tube and or fitting.

Model # is FFHT2126LW2

Here are your parts
http://www.appliancepartspros.com/parts-for-frigidaire-ffht2126lw2.html

Unfortunately it does not show the ice maker.
So I cannot be much help.

Replace the water valve.
Also check the fill fitting at the back of the unit. It may need tightening or may be craked from freezing.

Where can I get the inlet valve part number from?
The part number on the unit inside the freezer is 241642501, model IMBD03-004.

Appliance pros shows two different fill valves for that ice maker model.
4318047 for single water valve, and 12001414 for dual valve.
Which one should I use?

I would say the single valve as you do not have in-door water.

To double check this just look at the valve in the unit.

I cannot find any info on the numbers you gave in your previous post.