Q: Car won't start although it turns over. Actually the starter keeps going until I manually turn the key back off. Also a click wh

Drove car to work this am and it was fine when I shut it off. Go to lunch and when I tried to crank it it started and ran rough for a few seconds. Second try it started but died quicker. Now when I try to start it keeps cranking until I manually turn the key back off. Will not start the engine though. Also there is a slight clicking / whinning noise if I turn the key to the first position (not ignition on with lighted dash but just the first position) and clicks a few more times even when I turn the car completely off. Last time I checked the battery was fine at 14.4v so I don't think that is it? Going to try to hit the starter with a hammer while the ignition is on and see if this works but I'm thinking it is most probably a starter relay or the Bendix is stuck in the starter? Agree?

My car has 120000 miles.
My car has an automatic transmission.