Nokia Cark91 stopped registering as handsfree

I got a second hand car last year, which had a Nokia hands free cark91
installed.

Initially it worked fine with my Nokia 6210. At some point however (I
use the car very infrequently, and the phone even less often), it
stopped working. When the phone is placed in the cradle, it registers
that it is charging; but it doesn't switch to handsfree mode (It
really doesn't; that is, the display doesn't change; and when a call
comes in, the external speaker and AFAICT the external mic are not
active.)

I've tried very briefly with someone else's compatible Nokia, with the
same result; so I believe the problem is probably with the car kit, not
the phone (which is also secondhand and elderly).

I can't see anything obviously wrong with the contacts.

Are there known faults that can arise with these symptoms? What's my
next step to investigate? Or is it likely to be something unfixable?

Thanks in advance for any help or suggestions.