Theft Light

I have a 2000 Ford Taurus that ocasionally will not start. The starter will run, But just will not turn over. Recently my wife noticed that if she hit the gas a white puff of smoke comes out of exhaust and the car starts.
The anti theft light comes on while driving and the car tries to die.
The dome light sometimes doesnt want to go out even when the door is shut. But most of the time the car runs fine with no problems. Could this have something to do with the chip in the key ?

Sounds like the car has an electical fault, possibly an intermittant ground. My $0.02: have it checked by a reputable electical shop, preferably one with a factory trained mechanic.

BTW, does the problem occur with both keys? Given the dome light issue, the problem is unlikely to be the key.

If the starter runs but the engine will not turn over is a starter or starter engage problem. Is that what you mean??? White smoke out the exhaust usually means water in the cylinders.

are u using the oe transponder key?