theft light on consistantly and car still runs fine???

I was having problems with car shutting down at idle and then hard to restart. thought it may be the switch in the pass lock system so i replaced the swith lock cylinder but the car still stalled. Now I have put the old switch back in and the car will not relearn the key the theft light just stays on consistantly, i guess I could have loosened a wire or something??

also will this hurt to leave it on it is not blinking never.///??