flashing new message light when call has been answered?

It may be a hardware fault - remotely possible a software fault but most probably a broken logic gate inside an Integrated Circuit.

To solve the problem will require replacing the defective component - once you know which particular chip it is.

I doubt anybody here knows the circuit well enough to advise you - I doubt that anybody anywhere does either.

I don't think there's a factory-default-settings button but you never know - have you scanned the user guide?

Good luck...
April 2015