Relay. It's one of the ones in the box under the engine compartment. The one you pulled out in the engine compartment to shut it off is the one that is bad or stuck.
Replace it and you should be fine.
It's kind of hard to explain but i have an intercooler and the i/c pump i have wired to this relay.1 wire going to it. That way when ever the ignition is on the pump is on. it's temp. for the moment.
It's kind of wierd because with the wire shoved into one of the sockets for the relay and the relay then inserted in like normal....If i tighten the cover lid on to much for the under hood fuses it will make the car stay running and do the same thing that is happening to you.
So thats why i say it's the relay. Hope that helps in some way