Sorry, but your opening post does not make sense.

First, you say it won't engage the starter - then you say it engages the starter three times and then nothing. If it cranks three times then nothing, either the SKREEM is bad or the ring around the key is not reading the chip in the key fob.

Go ahead, take it to a dealer, it's only money. History has shown us they won't be able to fix the car, but they will sure charge you a lot of money. Let me restate that, IF it is a SKREEM, then good - cause that is their answer for everything.

Tell your "engineer" friend to simply download the service manual, follow the diagrams, and isolate the issue. If the relay for the engine control module on the RCM is bad, it is easy to track that down with a simple DVM.

If it is the SKREEM, well, the only way to really prove that is to replace the SKREEM - but I would not do that unless I was sure it was the SKREEM.

Again, if you can clarify which kind of "No Start" you have, we can get to the bottom of this easily.