Given that you have replaced the ICU my suspicions would centre on the Hall effect unit and the connector under the front cover.
The Hall Effect Unit operates on relatively low voltage and very low amperage, any corrosion, even corrosion you can't see will stop it dead.
In other circumstances I would also suspect the ICU and the ICU electrical connector, but with a new ICU you have positively eliminated that as the source and the make/break on the connector pretty much eliminates that too.
The first step I'd make would be to open the connector under the front cover and gently clean the connectors, give them a squirt of CRC and make break the connector a few times. You have obviously had experience with the JPT type connector given you have replaced the ICU, be aware that due to its design and the heat under the front cover, the connector there redefines the meaning of the word FRAGILE. However, if you do break it simply replace it with any three way auto connector that takes your fancy (or even three bullet connectors.) I'd give the ICU connector a spray with CRC on principle.
If that doesn't solve the problem my next step gets a little more complicated.
First make a Hall effect tester, you need a 9 volt battery, a LED, sundry lengths of wire and some alligator clips.
Next remove the Hall Effect device from the engine and set up on the bench with your tester and verify that it works.
Next set your wife's oven (it helps if she is absent when you do this) to 100 degrees centigrade and let the hall effect device bask in the oven for 20 minutes - retest the hall effect device, if it doesn't work you have diagnosed the problem, if it works, replace your coil.
I've left the coil till last because frankly there is no practical means of testing it (although you could rig a test rig and measure resistance when hot and cold and see if it will throw sparks when hot, but frankly it is just as easy to isolate it as the fault and then replace if it is "the last man standing".
If you end up having to replace the hall effect device it is doable, if you have a friend who is a bicycle mechanic and who will lend you his chain-breaker, you are going to have no problems getting it apart. If by any chance your bicycle mechanic friend works on Campagnolo 11 speed chains then you are in 7th heaven becaus ehe has a tool taylor made to insert and peen the new rivet to hold the Hall Effect device in the bean can.
Of course you can also use the Seimens HKZ 101 device and use small bolts to hold it. Your choice and I guess, what you can find.
The HKZ is not as robust a device as the original Honeywell device simply because it does not have high temperature wiring/insulation, but 1,000s of peopel are usign them happily (and if you use bolts they are a 15 minute job to replace anyway).
Please let us know how you get on.
