Thanks for the advice Gilly, the ignition switch did come to my mind because there was a problem with it when the car was new, that was fixed under warranty. Your assessment kind of makes a lot of sense, because what is the chance of 2 different components (starter relay and fuel pressure regulator) failing at the same time to give those symptoms during the same period of time, right?

So it's one bad component giving 2 different symptoms!

Is this a DIY job? does it require any special tools?

Thanks again.