As Frigilux says ... it's all guesswork until you know what temps are being attained in each section. The fresh food section apparently is not getting to freezing, you've not reported that as a symptom, and now say that the compressor is cycling so that infers the thermostat is at least working in that respect.
Assuming the thermostat is in the fresh food section and the freezer control is an air damper, then the way the unit works is that the compressor runs until the fresh food section is at the selected thermostat setting ... with the freezer temp moderated indirectly per how much airflow is directed to the fresh food section. I.E. less air to the fresh food section (freezer control set colder) gives a longer run time for the fresh food section to reach the target temp, which in turn gives more run time to drop the freezer temp. Freezer control set to the warmer temp, more air goes to the fresh food so it cools faster which gives less run time to drop the freezer temperature. The fresh food and freezer section controls are adjusted together for the desired results.
Possibly the freezer control is broken, not moving the air damper?
Also check that the condensor (on the bottom behind a kick plate?) is clean. Odd behavior can result when it's clogged with accumulated dust.
I've heard recommendation to keep the freezer temp at -5°F to avoid ice crystals forming on ice cream ... but I rarely buy ice cream so can't say from experience.