01 Ford Taurus Won't Start

Shouldn't be the evap. That mainly vents the gas tank http://www.aa1car.com/library/evap_system.htm To me it sounds like either the alternator isn't putting out or there's a parasitic drain on the battery. To test the alternator, quick way would be to get a multimeter and set it to 12 volts DC and put the positive probe on the positive of the battery and the negative on negative. Start the engine and the battery should read over 14 volts because it's getting charged by the alternator. If it isn't then it's a good chance it's the alternator. If it does, then the battery is weak because perhaps some small circuit that remains on when it should shut off.

check a power drain from dash lights,door lights, over head lights etc. if its not the alternator. you said no lights when it fails to start?? do the head lights flicker when it cranks? are the battery posts clean? and connected tight?