My engine block heater has worked for me about three times so far this year. Those were colds nights during which the car didn't need to be heated anyway, but I decided to do so just because I could. Last night I tried to do the same but in the morning the engine was still cold after three and half hours. Is there any means by which I can test to find out if it is just the cable/the connector that stopped working, or if it is the heating coil embedded in the engine block that's faulty? Additionally, considering that my car has been in this cold winter area all its life, is it normal for the coil to stop working by now? I'd like to replace whatever needs replacement before the really nasty weather arrives. Thanks all.

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1999 Mercedes-Benz S600, 103K miles - garage queen
1988 Mercedes-Benz 560SEL, 89K miles - daily driver
2007 Hyundai Sonata Limited, 31K - daily driver