Here are your parts
Replacement parts for FRIGIDAIRE NGS26ZZAW3 Frigidaire/refrigerator | AppliancePartsPros.com

Here is a tech sheet
http://manuals.frigidaire.com/prodinfo_pdf/Anderson/240389604.pdf

If transported on it's side did you leave it 24 hours before plugging in.

If compressor is running constantly, remove the evaporator cover in the freezer so you can see the coils.
If they have some frost but it is blotchy or if it just has frost in one area usually where then freon enters the coils then probably you are low on freon.
If there is no frost either you are out of freon or the compressor is toast.

If the compressor is cycling you may have a thermostat problem.

[COLOR="Blue"]How could it be the compressor or the thermostat if the freezer and refrigerator are working? [/COLOR]
Yes.
Your freezer is not working correctly.

[COLOR="Blue"]the refrigerator works fine, the freezer is cool but not cold enough to make ice.[/COLOR]
If the freezer is not freezing the odds are very high that the fridge side is also not working properly as it is getting it's cold air from the freezer.
Measure the temperatures in the units.
Freezer should be around 0 degrees F
Fresh Food side should be around 40 degrees F

[COLOR="Blue"]Is there anything that would affect the temperature of the freezer only?[/COLOR]
Yes but if the freezer is too warm then the fresh food will also be too warm.
The evaporator coils in the freezer does all the cooling.

[COLOR="Blue"] If it was the compressor, wouldn't the whole thing stop working?[/COLOR]
Only if the compressor is toast.
If just low on freon it will not cool to where it should. there are also other things that can cause poor cooling.

Here are a couple good sites with basic fridge repair/troubleshooting help
http://www.applianceaid.com/frig.html
Refrigerator Repair Guide: How To Fix a Refrigerator - ACME HOW TO.com