The ignition switch can sometimes be a problem if the connections or contact points on the switch are pitted, corroded, burnt, or anything else that could decrease the power going out of the switch. If you have 12.5 volts at the battery, and the ign switch is faulty, you might be getting a lower voltage on the other side of the switch, maybe not enough to operate the computer. Many cars have a fail safe that if the battery voltage drops below a certain level the computer will shut off to protect itself. Usually around 11.5 volts.
To check the crank angle sensor you need to back probe the crank sensor wires at the dfi module. The 2 wires on each side of the 7mm bolt at the module are the 18x and 3x wires. Black wire on the multimeter goes to battery earth, the red wire goes to either the 18x or 3x wire. With the ignition on, turn the motor over by hand (ratchet and socket) and you should see battery voltage at the connector flash on and off as the reluctor ring on the back of the balancer passes over the crank sensor. 18 times per full 360 degree rotation (18x signal), and 3 times per full rotation (3x signal). No voltage reading or constant voltage that doesn't change shows a faulty sensor.
**Before you start this test make sure the pull the fuel relay to prevent the car accidentally starting when your turning it over.
An even easier way to see if the sensor is working is to hold the injectors when the car is being turned over by the starter motor. You will feel them click. Or plug a noid light onto the injector wiring.
Also Is the immobiliser light off when cranking ?
