1992 Ford Escort starting

Other Category problem
1992 Ford Escort V4 Two Wheel Drive Automatic 92000 miles

My daughter has a 1992 ford escort. She said when she stopped the vehicle began to rev up. She said she put it in reverse and removed the key and the vehicle stopped.

I looked at it today because she could not get it started. At first the key would not turn, eventually we got it to turn. I also replaced the battery because the green window was black and the car did nothing at all when turning the key. After replacing the battery all the exterior lights turn on and when turning the key the panel lights come on (check engine lights etc). The vehicle does not turn over at all. I do hear a whirring and a click coming from under the dash on the right side of the car near a black circular box. Also with the key in the on or acc position, the radio and the heater does not turn on. Although the the beeping from the key being in the ignition is chiming. The beeping also continues when key is removed, somtimes.

Any ideas on what this might be. I had one suggestion of the starter, if so where is it on this particular model?

Thanks for any help you can give.