A model n umber may be helpful even thogh I do not have access to GE tech info.
Find your model number - AppliancePartsPros.com

I cannot say what the noises are that you hear.

First check that the compressor is turning on.
You can usually hear it but you should also be able to feel it vibrating.
It should come on and stay on until the unit reaches the set point temperature though the unit may go through one or two defrost cycles in the 24 hours.

Check that the condenser coils are clean and the condenser/compressor fan is running and clean.

Check that the evaporator/freezer fan is running.

If on remove the cover in the freezer and check the evaporator coils.
They should have a fairly even coating of frost on them.

If there is frost only in one area usually where the freon enters the coils then it is a sealed system error and is probably not worth fixing.

Note do this test after it has run for about half an hour. If you do this during or shortly after a defrost cycle you may come to the wrong conclusion.