It is very possible that a broken speedometer cable might cause the symptoms
you describe.  I had a 92 Isuzu Trooper that had a speedometer cable which
intermittently stuck which caused all kinds of other problems when the
speedo wasn't working. Apparently the engine computer makes adjustments
based on vehicle speed and when it wasn't getting a reading it made
incorrect adjustments to the engine management which caused numerous
drivability issues.  Since the Check Engine light predominantly reports
emissions control problems it is quite possible that the engine computer
thinks that the emissions levels are out of the range they should be when
going "zero" MPH as your speedometer is reporting.  I would suggest fixing
the speedometer and see if the other problems clear up, I suspect they will.
You could also have the Check Engine code read (Auto Zone will do it for
free) and see if the code supports my theory.