What happened to me once is the area on the starter where the terminals are cracked. It happened when I went to start it up and when it started, I released the key but the started stayed engaged so I shut off the key. Engine shut off but the starter kept going. Is that what's happening?
There is a start position on the key switch and a run position. The start position could be bad. The solenoid could be bad also. I would check it first. Did you check with the ground cable as Leo suggested?
Unplug the yellow wire at the relay on the inner fender. That will stop the starter from turning on while you test.(if the ignition switch is the problem) Check for power at the yellow wire. It should only have power in the START position.