2002 Impala starter keeps running after engine starts

2002 Impala 3.4 engine.
The car had a bad positive battery terminal and bad battery. I replaced them. Then a few days later it wouldnt start. I had a used starter from a year ago when I was trying to fix it, so I replaced the starter. It still would not start, the security light was flashing. I learned about reprogramming the key and did the wait ten minutes 3 times to reprogram the ignition. The car started but the starter kept running. I put the other starter in, same thing, the starter does not stop running.
Its possible I got the wires wrong. There are three of them. A tabed terminal that only fits in one place. Another wire I placed on the other terminal. A small wire that goes to a small terminal. I have looked and looked online and cant find if the wiring is right. If the wiring isnt right, is it the ignition? I replaced the ignition switch about a year ago. Strangely I didnt have to program it then.
Thanks for any help in advance.