How old is the battery ? If several years then get it tested, when mine was on its last it would struggle with a cold start but be fine once the car was warm, the starter motor was the same. It could take ages to start (sometimes mistaken for a duff battery) when it was cold but again be fine when it was warm, the injectors won't fire untill the engine is being turned over at 750 rpm.

As said above, carry out as many checks as you can to narrow it down. I've read several threads where people just through money at a problem and replace costly parts only to find it was something simple like a fuel filter or a battery !

Good luck.