I 2nd that when engine turns over when engaging the starter with the key, but the engine fails to stay running, and will not turn over (rotate) again after the "third" try, it's the SKREEM.

I never had a SKREEM problem but the CPS failed on my coupe. The engine would turn over all day with the starter engaged but it would not start and run by itself. The problem would be intermittent and would more often work when the engine cooled down. New Bosch CPS fixed it.