New starter, battery, and alternator is good. What could this be? I also replaced the distributor cap last year when I had the same problem, and it seemed to fix the problem, but only temporarily.

 

I had a hairline crack in a distributor cap cause the same problem. The car would start but run really rough & misfire. I couldn't even see the crack until I took the cap off to replace it. You may want to check coil / plug wires closely for this. You may also want to look for poor or corroded terminations on starter.

 

Did that last post put you in the correct direction?

It is true, both the distributor cap and the High Voltage Ignition wires can get pourous over time; and absorb moisture during damp / rainy mornings. thus keeping the car from starting.

This can be easily tested (at this point) with nothing more than a spritz bottle.

With a fully warmed up engine, start spraying the wires first - working towards the cap.
If you've a problem, the engine will start missfiring and possibly stall.
The heat from that pre-warmed engine will dry the wires off (however), so you should be good (after sorts) to go to the local Death Zone auto parts store for your new Cap, Rotor and Wire Set.