The fridge is not getting any gas obviously. I have fixed that on a couple of fridges. You take off the gas pipes at the back and soak them in mineral spirits so they are clear of any gunk. The sprayer on the end of one of the pipes just before the "burner" needs a soaking especially. (use a taller sort of glass jar to dunk it in)
When that is done right, you can pour spirits into the end of the pipe the sprayer is on the other end of, and blow on it like a straw, and the sprayer will squirt like a little water pistol, indicating it works.
One part that also can block the gas even if free of any gunk by that cleaning, is the solenoid valve that is before that sprayer tube part. It has some wires to it. I have had a situation where a wire was not on it properly so it would not open. Fit the wire on right and it works! All this is easy to get at behind a fridge.
Can't help with that furnace, but it seems it has to be pulled out to get at the burner part that might need a clean-up. But with no spark either, it might need electrical work.