On some cars, the Vehicle Stability Control warning light will come on along with the Check Engine Light (CEL)--for reasons that escape me. The need to replace a catalytic converter and/or having a faulty gas cap are both situations that would trigger a CEL (and possibly a VSC warning light), but if the CEL is burned out, you would not be seeing the full picture, so to speak.
Step One: Verify that the CEL light is still operative! When you turn the ignition key to the "on" position (the position before the "start" position), the CEL should illuminate briefly. You may need to do this a few times to verify whether the CEL is still working.
Anyway, my thesis--subject to revision--is that you CEL may be burned out. If the light is burned out, you would not be aware that one or more systems on your car are not operating properly. If the CEL is burned out, have it replaced.
If you have the car's OBD system scanned for trouble codes, that will give you indications of what systems on your car are not working as they should. Whether the CEL is burned out or not, it is possible that the OBD system has stored trouble codes. It is very possible that rectifying the problems leading to OBD trouble codes will cause the VSC light to go out.
Check the CEL and have the OBD system scanned for trouble codes, and then come back to this thread to report your findings on both issues.