I installed a remote starter on that car several years ago. That module was my first suspect on the list. So while the engine was still running (with the key in my hand), I disconnected all the connectors from this module.... Nothing happened, the engine kept running. Then, I went on to disconnect the key switch harness after removing the cover under the steering column.... Again, nothing happened, the engine still kept running....
So, it doesn't look like the remote starter module or the ignition switch is at fault. There must be a relay or something that sends current to the ECU and fuel injectors even when the key is off!
