If the light is still on then the problem was not the battery but was instead the alternator which is more than likely defective.
You do not reset a battery light. The light is on because there is something wrong with the charging system on the vehicle. In most cases the alternator has failed and needs replacing. Once you fix the problem that caused the light to come on the light will go out.
Clean both battery cables and check the connections on the alternator. If it continues, go to auto zone and have the alternator checked.
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.
The vehicle should ave a voltage regulator. If the battery and alternator are good then the regulator is most likely bad.
You possibly have a loose alternator belt or the alternator is weak. Check the voltage at the battery with the engine running. It should be 13.5 ? 16 volts. Any less and the alternator is weak and needs replacing. Also make sure the connections at the battery are clean and tight.
You either have a battery that has a dead cell and needs replacing or something is on pulling power from the battery. Can be any light on the vehicle or a stuck relay. In rare instances a defective alternator can cause this.
Replacing the battery was not likely the cause of your check engine light. Most auto parts stores have a code reader will read the code for you at no charge and reset the light.
go to your garage and make a battery and charge test, probably a charging problem
go to autozone and have them do it it is free. or try disconnecting your battery for a few mins.
Why would battery light come on then go off
turn the steering, full lock to the left, then full lock to the right, while being stationary, light will then go out.
Dead cell in the battery which will mean it needs replacing. Can also be something is on drawing power from the battery. Any light bulb, or an stuck relay. Check all lights and then all relays.