Major Car problems, help needed :(, Car engine died... Options

[rentaspace]

Well, started last night, had just finished a National Park Run (Windy roads), I didn't push her too hard since I had GF and her sister in the car. Drove approximately 110km. Got back to my mates house, turned the car off, went inside for about 10minutes and then got back into the car to go off to his GFs house (approx 20km away).
As I was driving around a small roundabout, the engine died... Turned straight off, and I coasted her to the side of the road, where she wouldn't start again... CEL was also brightly illuminated. The starter motor clicked but the engine would not turn over...
I called my roadside assistance and got them dispatched. Using a hammer on the starter motor, I got the car to turn over, run for 10seconds and then die again...
Roadside assistance arrived twenty minutes later, and the car started, but had a really strange noise coming from under the black covers at the front of the engine. (kinda like a clicking/grinding noise).
I decided that I did not want to drive it on the highway with the possibility that the engine could just cutout, so I decided to get it towed to the destination we were heading (I get 8km free towing per job/problem):



The driver complemented my car and said it's the nicest celica he has ever seen, which was nice
Anyway, slowly backed her off the truck at the destination and once back on the ground, started the car and moved it to the parking area... We went inside and I went to bed cause I was pissed off haha.

Next morning, woke up and my dad had arrived to inspect the car. Everything looked fine, the car started first go and sounded normal... Alright, so we drove her from Engadine to Barden Ridge where I live, she drove fine, no weird noises or sounds and held power as usual. Drive into my driveway and pop the hood, I can hear the weird noise again from the same place...
Turn the key off, and back on and she won't start again... I also noticed that now today when it died, every Warning light illuminated (exactly the same as the test when starting the car)
So it seems, when the car is up to normal temperature it won't work, but when cold it's fine...
So far, the roadside assistance checked the battery and plugs and leads. He couldn't run a diagnostics as the CEL had gone off before he arrived...
Any Ideas what could cause an intermittent issue like this? (I have been told to check the fuel pump, but I do not think this is the cause)
Any help would be greatly appreciated...

[Special_Edy]

No, the IAC does not increase the throttle when the AC kicks in
There are two Idle Up Control Valves, one for the AC and one for the power steering.

The AC one is bolted to the passengerside of the intake manifold. It is a small electronic box with 2 or 3 hoses coming out of it, probably just to the rear of the vacuum diaphram on the end of the fuel rail.

I had to replace mine, I could only find an ST one at the junkyard. It works perfectly but the mounting bracket is different.