I'm still having the same problem. When the engine gets hot, something in the electrical system is preventing the starter relay from getting a ground. As far as I can see the ground comes from the immobilizer unit, why it come from there I don't understand. I have changed the starter and the engine ...

I have the same problem. I can't figure it out either. I'm leaning towards the security system in regards to the key code to computer. You might want to try a different key. I know you replace it already but it's still worth a try.

My car has the same hose. I believe that hose is for the A/C condensation drainage. I to do not have anything connecting to that brass fitting. So I would put that hose back where you found it. Sorry I don't have any thoughts on fixing your problem. I will have to think about it.
Good luck.

I have a similar problem. I go to start the car and it will not start. The car has power but the starter relay will not activate. I'm in the process of troubleshooting the problem. I suspect the starter switch. I will let you both know if I figure it out.