Is the fan bad in my laptop? (picture included)

From reading a couple old threads here, I am starting to think that my laptop turns off randomly because of a bad fan. So I checked under my laptop, and I can't feel air flow from anywhere, nor do I see a fan spinning.

I have a satellite a105-s4284. I am including a picture of the bottom of the laptop, where I have circled where I believe the fan to be. It is not spinning. Should it be spinning at all times, at least to some extent? If this is where the fan is located, then I definitely need to order another one.

Thanks for the help!

ugh, well i can't post a picture, because my post count is too low. but just confirming that the fan should be spinning at all times should suffice.
 
if the temp is cold the fan sometimes stopped.

but, for all laptops, when you turn them on, the fan should spin, no matter the temperature is, for few seconds.
 
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