CE lamp means an emmissions fault has been detected, but lucky for you, that car has owner access to codes under the hood .
Black box w/lid, foward of battery.
There is a sw/LED that , when pressed , will Flash back a code [number of flashes].
There are a ton of articles in the archieves on the exact procedure....
Once you have the code info, post it and someone will tell you which fault has been detected and possible remedies...

PS
Are you also saying the CE is ON even with the Key in the OFF
position ?????