Check that the fuel pump is working correctly as that could cause it if the pressure starts to drop off.
A thing to bear in mind when you do get it running is that if they have been stood for a while the valves tend not to open properly and it will run like a bag of shit till it gets warm. other than that i think your on the right lines with the ICV. If it were the crank sensor the car wouldnt start at all though as it wouldnt be getting a signal pickup from the flywheel.