Can anyone help me?

I have a 1991 Honda Accord. There is a green "S" light on the dash to indicate overdrive which is activated from the shifter. This green "S" light (S for sport) is flashing repeatedly once you put the car in gear. In addition, the speedometer, odometer, and trip meter all stopped working and the "Check Engine" light comes on after 5 minutes and does not go off. Once you shut the car off and restart it everything is fine for a couple of minutes and then the process restarts again. I tried disconnecting the negative batery cable to clear the codes but the problem keeps returning. My QUESTION is: will a broken speedometer and odometer cause the check engine light to go on in this car. It would seem VERY coincidental that all 3 of these problems would happen at the same time. Also would the malfunctioning speedometer cause the overdrive light to flash incessintly. Thanks for any help that anyone can provide.