What does the red light saying Check Engine mean when it comes on after my 1992 F-150 Ford Pick Up warms up?
It could be the temperature sensor you would have to see what code is tripping.
What is wrong if the check engine light comes on at idle and the engine run rough on a 1994 Mazda 929?
Replacing the battery should not have triggered the check engine light. The check engine light comes on when there is a problem with the emission system. Saying that, I would drive it for a while to see if the light does go out. If the light does not go out have the ECU scanned to retrieve the trouble code. Then use this code to diagnose the problem.