Yeah, if she hasn't got a clue, don't bother letting her in. Show her what the black book value of the car is (probably around $1,500) and tell her you'll be kind because its a clean example and offer her $2,500. If she laughs in your face, you know she's a little more "aware" than she lets on. If she hims and haws about it, you know you're probably in the right ball park.
...and since she got it in the divorce, don't feel bad about low balling her. I'm sure like most women, she made out like a bandit in the split with the hubby and it was probably his car to begin with.