Amana SCD25JL

Hello everyone,
    Today our Amana refrigerator has stopped producing any type of cold air. I have removed the back and cleaned it out as it had a lot of dust. When I try to turn on the freezer, I hear the blower come on but the compressor is not starting. Is my compressor bad, or is it a relay somewhere which could be faulty? I don't have a lot of experience fixing refrigerators, but I have taken apart and fixed a blower in a Maytag dryer; I just need a little guidance as to where to look.
Thanks in advance, Nick
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On a follow-up note,
    I turned the freezer dial all the way up and heard a clicking sound then the lights did dim a bit for about 10 seconds. After that I heard another clicking sound and the lights returned to normal. I'm assuming that the compressor has gone bad and the relay is good.     If this is what everyone agrees on, is this something that I can do myself?
Thanks, Nick

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