03 Eclipse Spyder GTS 3.0 Will crank but not start

I have fought with this car tooth and nail for about 8 months. After purchasing the car I thought to do some general maintenance so I replaced:
Timing Belt - Crankshaft Sensor - MAF Sensor - Distributor - Plugs (3 Sets) Current set is NGK Iridium IX Part No. 6418 - Wires - Fuel Pump - Fuel Filter - Radiator (previous was cracked) - Valve cover gaskets - Oil/ Filter - Coolant

After all of this maintenance and multiple start attempts over the past 8 months it still has a hard start. Some days it will start first try but more then 80% of the time the car just will crank and not start. I noticed after having the battery charged and reinstalled the headlights flashed for a minute or so. I do not know if this is related. If anyone has any insight on this issue I would greatly appreciate the help.
thanks

 

Definitely could be alternator. Or get a computer you plug into the dash like they have at autozone. Run it primarily to check for sensors. Sensors will screw the whole car till you replace them.