Here is a link to a good site with basic fridge repair info.
http://www.applianceaid.com/frig.html

First you have to determine if the compressor is running. You can usually hear it start up, also you should be able to feel it vibrating and it should be warm.

Also cherck that the fan in the freezer is running.

You can have 3 compressor conditions:
Always on: Could be a sealed system problem. If there is at least some cooling it may be low on freon. Both will be expensive repairs.
Also may be a defrost problem.

Never on: Could be a control thermostat problem or a compressor problem.

Cycling: Could be a compressor start device or the compressor itself, often you can hear a clicking noise. Could also be a thermostat problem.

Here are your parts
Replacement parts for AMANA DRS2660BW REF - SXS/I&W | AppliancePartsPros.com

[COLOR="DarkRed"]After using a vacuum to clean up the filthy coils, would it solve the problem?[/COLOR]
A long brush also comes in handy here.
Remove both the front kick plate and the rear cover.
Cannot say if it will solve the problem but it may. A long shot but worth a try.
Clean them and also check that the condenser fan is running and the evaporator fan is running. Usually dirty coils will result in poor temperature but not reduce it to just cool in the freezer.
If the compressor is on and both fans are on then you will have to remove the cover in the freezer so you can inspect the evaporator coils.

Heavily iced/frosted over coils is a defrost problem.

No frost or just frost in one area is a sealed system problem and you will need a pro , also it will be expensive. Often it makes m,ore sense to put the dollars towards a new unit.

Be sure to check them after the unit has run a couple hours because if you do it shortly after a defrost cycle there may be no frost.