two things..the ignition switch its worn out and need replacment or the selenoid inthe starter its going bad, need to replace starter,one or the other,,
Could be defective stater solenoid that is not releasing
Starter solenoid is sticking. Replace it.
the starter should not stay engaged after the vehicle is running. more than likely the armuertor or the bendix is faulty. replace the starter.
Sounds like a bad ignition switch. It could also be a bad starter solenoid. If you can find the solenoid you can unplug one of the small wires while it is trying to crank over and see if it stops. If it does it is probably the switch. If it doesn't then it is probably the solenoid.
solenoid broken
Either the ign. switch is faulty, or the starter is faulty Or the starter solenoid is stuck closed, so the starter is constantly engaged and getting voltage from starter relay. If so you would need to replace the solenoid.
If your starter stays engaged it is either your stater relay (solenoid) or your ignition switch.It is usually the relay,either mounted on your inner fender(earlier system)or on the starter itself.Follow the positive cable (red) from your battery,if it goes directly to your starter it is the later system.To test disconnect the ignition wire on the relay,the small gauge wire.If there is 2 small wires on the fender mounted relay you can disconnect them both if your not sure witch is ignition wire.Leave the 2 large wires connected.If it still is turning over it is your relay,if it stopped it is your ignition.If you have the stater mounted relay remove the small wire from the "S" terminal,and repeat as above.
Bad relay
Worn ignition switch? Check to see if it has a rod connected to ignition switch at the lower end of the steering column--may needs adjustment
That sounds like a stuck relay.
If this happened immediately after replacing the starter, I would say the wires on the solonoid are connected wrong. It could be the switch but I think it is the wiring.
You need to replace your ignition switch. I had the same problem on a Ford f-150 and that's what it turned out to be. Does the starter stay engaged or does it disengage itself? can you turn the key switch and nothing happens once it has started