After moving our fridge, it will not cool. Fan is turning but compressor does not seem to be running.

check the heating element

possible bad cooling unit low on freon or compressor bad

Many Amana model fridges have the freezer fan wired through the bi-metal thermostat that is clipped to the evaporator. Either your compressor has a bad start device and that is why it is not cooling, or the compressor IS running and the unit has lost its refrigerant charge. Running compressor with no cooling = buy a new fridge.
Compressor hot, but not running = start relay replacement to get the compressor going. Start Device 8201786

Try this test. Set a window fan behind the fridge to constantly blow air across the lower coils at the floor. If the fridge works well after a while of this, then the lower fan on the fridge needs replaced. Sometimes though, after a while, the fan will finally start working again because the cycle has finally corrected itself with the test. Leave the window fan run on low for a few days before removing it. The hum you hear is the compressor moving the coolant and is supposed to do the hum sound. That's good. Now once the fridge is working, and you still have a good freezer section and not cool enough below in the fridge for you, there is a knob that sets the cool lower by opening flaps under the freezer to let more cold down to the fridge area. Set this knob to colder and the flaps will open more.

if they are both cold, but not cold enough, one of two likely scenarios, one minor, one major. the major one, you haev a sealed system leak of refrigerant, several hundred dollars to repair.

the minor, your condenser fan motor is not running, its job is to cool the compressor, if its not cooling the compressor, when the compressor gets too hot, it will shut itself down, while the fridge continues to run. when this happens, the unit seems fine first thing in the morning, but by evening it seems less fine...while everyone sleeping, doors have been closed, allowing unit to "catch up". replace fan motor.

Most modern combination units have two fans; one under the cabinet to move air over the coils and a second concealed behind the cabinets to distribute the cold air to both compartments. When you balance them to get the desired temperatures in each, you are adjusting the air flow from the cooling coils. Typically, the freezer has the coils and the fridge gets a little via ducts in the rear wall. If this fan fails, the freezer will suffer least and that seems to be what you are experiencing.
When the compressor is running, check the inlets in the back of the refrigerator to see if you have noticeable air flow. If not, that fan has failed.

You have a refrigerant leak. Your coil in the freezer should be frosted. You're looking at 600 dollars minumum for repair.

hi u didnt rate for my chat?

Check the back wall of the freezer for ice buildup.
If yes, a defrost parts problem.
Check the freezer fan. Is it running?
If no, replace the freezer fan.
Check the condenser fan at the compressor. Is it running?
If no, is compressor hot?
If compressor is hot replace condenser fan motor.
If compressor is not hot.
Replace the compressor start relay.