I have exactly the same problem, on exactly the same fridge as yours. The light kept flashing, I bought a new bulb, but made no difference, so we thought it must be the switch, so found one online, and that came today, my husband put it in, and it was fine for a while, then it done exactly the same as before, the fluorescent tube kept flashing, but now nothing happens. Getting a bit fed up with this fridge. Hoping somebody can throw some light on the problem. Like you I can hear it clicking. We wondered if there was a starter on the tube, like there is on ceiling fluorescent tubes.
Wendy Haynes, November 2010