I recently replaced my starter and solenoid. Then I drove it locally and the starter stayed engaged. So I replaced the starter and solenoid again. I drove to the store and shut it off. When I got home, I shut if off but the starter continues to run. I pulled on the battery cable and it stopped. Not sure what shook loose Is there a starting point? Is this a common problem?

 

Most of the time, it's a faulty solenoid but since you replaced that, I would make sure you do not have 12v being supplied all the time to the small terminal on your starter solenoid. You could try pulling the connector off to see if the starter stops. The ignition switch supplies that feed to the solenoid.

 

There are several wires connected on the right side of the solenoid with the lead to the starter. Do I need to look at them?

 

Sounds like you hooked up the solenoid wrong. One big terminal should have JUST the starter lead, one small terminal should have the small signal wire, and the other big post should have everything else, including the positive battery lead.

 

Left side is only lead to starter. Right side is from positive battery with several other leads. Upper middle is ignition starter lead.

 

The starter cable has worn against the battery box and must have grounded the line, keeping the starter running. I could be totally wrong!