1st.. I am trying to find the exact (or closest) Frigidaire model number for my Kenmore French Door fridge (253.70313211)

In diagnosing a problem, I found what I will call a strange design (flaw??).

The fridge quit dispensing water. You could hear the valves click and buzz but no water came out.

I performed the normal diagnosis.. I rang out the water valve coils with an ohm meter, no problem.. I checked the signal at the valve(s), no problem. So.. One would think it was a bad valve (mechanically).

Then I noticed that it also quite making ice. The ice maker is in the fresh food compartment. You can hear it drop the ice, then a few seconds later you can hear the fill valve(s) click and buzz.. No water to the ice maker.

One valve (water dispenser) goes bad.. OK.. Two at once (water dispenser & ice maker fill), pretty rare so I did some more digging.

The valve assembly has a total of four valves.. One main valve (main water supply => to filter), a yellow valve (water dispense), a green valve (fresh food ice maker), and a blue valve (freezer compartment ice maker). I do not have an ice maker in the freezer compartment.

The water line from the filter goes into the fridge from the back next to the blue freezer ice maker line (not equipped), then comes out. I am going to call this a loop.. In to the back of the fridge above the freezer, it seems to loop and come right back out. This line connects to the supply port for the other three valves.

I understand why the blue line is there even though not used.. I do not understand why the line from the filter goes in, seems to loop, then comes out and goes down to supply the other three valves.

Long story short, this line seems to have frozen and the plugged / frozen section would not allow water to go to the other valves.

I got everything working by bypassing the in and out loop. I'm sure if I had a place to put the contents of the fridge, I could have emptied it out, turned it off for a few hours and the line would have thawed out.

My boggle: What is this in/out for? I can see no reason it exists. What would make it freeze after 3 years of running with no problems?

Some of us would tell you to unplug it and come back in a few days. Depens on depth of problem and how busy we are.
If I'm nice I use a steamer to thaw things out, it is faster than a heat gun and less messy than hot water. You'll still have water to control but less at least.
Defrost drains clog or freeze for no reason, foreign matter, frost, etc... there may even be a seal kit for your machine's ice room because of a frosting issue. It's a constant issue in brands with an upper ice room. Once you get that drain flowing check the bottom end near compressor for any reaon it would not be draining properly.

https://smile.amazon.com...-22&keywords=steamer

Warning, the handle comes apart very easily right where you hold it, you do not want to be holding it there if that happens. Tape it or something.