Without a happy woman, the thing doesn't work (2,3)
I believe the answer is:
no joy
'thing doesn't work' is the definition.
I don't know anything about this answer so I cannot tell whether it can be defined by this definition.
'without a happy woman' is the wordplay.
I cannot really understand how this works, but
'without' could be 'no' and 'no' is found in the answer.
'woman' could be 'joy' and 'joy' is located in the answer.
No letters remain.
This explanation may well be incorrect...
'the' acts as a link.
Can you help me to learn more?
(Other definitions for no joy that I've seen before include "lack of success" , "Unsuccessful (colloq.)" .)