It seems unanimous that fuel delivery is the next thing to investigate. We just replaced the fuel pump in our 2004 Limited coupe to solve a hard starting issue that seem to happen more when the engine was warm. Ours has 37,000 miles on it and we had already replaced the fuel filter with a new BOSCH unit. I would recommend a BOSCH fuel pump but they run about $150 so I went with an off brand auto top one with good reviews on Amazon for $45. It seems the check valve in our fuel pump was not working properly to maintain system pressure when the engine was turned off.