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Sounds like the EIS itself is bad or could be the key. The ESL might be stuck, the EIS won't release unless the ESL has released first.
I doubt it is related to anything else you are suggesting like a loose wire or the alternator.
If you have the second key you could try that as a test.
When you insert the key are you getting any kind of an error message in the odometer area?
The ESP light is probably due to having the battery disconnected. Next time you get it started try turning the steering wheel all the way one way then all the way the other way a couple times, this will reset the steering angle sensor. You probably have to relearn the power windows and the sunroof as well, common things that happen when the battery is disconnected.
The ignition switch should not be affected by disconnecting the battery, unsure why you are having problems with all that.
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