It sounds like a fuel problem. I would investigate the fuel pump and injectors first. I had an issue with a bad injector that would slowly bleed down when the car was off for several hours. It would drop the fuel pressure and require longer time to start. In cold weather it was worse.

Really a had start issue should not be too hard for the mechanic to diagnose. Once he proves it will start, he knows it has compression, fuel/air and a spark. From there, he just needs to figure out why one of those components is missing at start up.