Not cooling. Fans, light running, compressor starts and stops with click noise

My refrigerator has been working fine so far - just been a little noisy. However, yesterday the freezer stopped cooling. I realized late when almost everything was defrosted. Today the refrigerator has stopped working.

Here are the symptoms:

  1. Lights and fans are working. Fans both internal and the one behind are working
  2. Fans can be started/stopped using the thermostat (switch to off or slide to right to increase cool)
  3. When I start the refrigerator from off position, the fan starts immediately. There is a clicking noise around 15 seconds later (I do not notice anything significant at the first click). Another clicking noise around 1 min later - compressor starts and 5-10 seconds later compressor stops with another click. The later cycle (compressor on/off with clicks) is repeated every 2 mins or so.

As I had mentioned earlier the refrigerator always was a little noisy, but the clicking sounds now are a little less subdued.

Please help.

Can this be a problem of the starter? Or the capacitor?
How can I check the starter/capacitor to see if the problem lies there?