Jeep starts with key in on position?

The two smaller wires going to the starter solenoid are backwards.

The battery terminal which connects to starter solenoid is connected incorrect or its loose.

Also inspect the other battery terminal which connects alternator,its loose or not connected.

In most cases,the starter battery connection is loose or not connected properly.

The two small ones that plug onto the engine side of the solenoid.

You are getting the 8v from the coil in the run position fed into the S terminal on the solenoid, thus energizing it when the ignition is on. Flip the wires any you will be fine.

The 'Small Blue' wire should be on the small 'S' terminal on the starter relay ('Solenoid'),
The 'Small Red' wire should on the small 'I' terminal on the starter relay.

solenoid on upside down.

One of out garage onsite customer  had the same problem,after he got the solenoid replaced.

At out garage we replaced the wires exactly as they were and mounted the solenoid back on the fender the same direction it was before. Now when we cranked the engine to start it, the starter would not stop cranking even if we pulled the key. 

Our garage technicians were confused,so we verified the wiring connections,swapped starters and starter cable,thinking it might be drawing so many amps that it was welding the solenoid internally. Same problem. 

So we tried this option and this helped,we flipped the solenoid the other end up and it started working correctly. The spring pressure inside the solenoid was not enough to release the connection.And that was causing the problem.

Quite possible.

But if all this mentioned here,is checked out ok in your case.

Then .........

There are bunch of fusable links on the passenger side under the hood, I suspect that it blew one. What is happened is you lost the 12volt run side. I suspect a blown fusable link. Bunch of green wire all attached together.

Inspect this mentioned possibilities.

This will help.

Thanks.

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