This is a clever little problem. To begin with, anytime a car won't start, you ask yourself two things: Is there fuel? Is there spark?
The spark comes from the starting system, so I would have that checked. You replaced the battery and starter, which is fine, but it could be the alternator. This could (perhaps) be the reason that it's harder to start after being driven for awhile, though I don't think that's likely. Even so, if there is an Autozone nearby, they'll check the whole system for free.
Personally, I think the problem is the spark plugs, but not being able to hear the engine or know how it behaves when you try to start it, I can't be sure. But that would help explain why it's harder to start after being used: The engine heats up and expands, the plugs get hot and become unseated or perhaps gap changes, and therefore they don't spark like they should.
However, if it isn't the starting system or the plugs, it must be the fuel delivery system. Maybe the fuel pump is bad or the fuel injectors. Here's a quick test:
open up your air intake so you can get air directly into the engine. Just take off the cover to the filter and you'll see the pipe where the air goes in. Spray a quick shot of Ether or Car start spray that you can buy for 2 dollars at Autozone. Spray it directly into that pipe while starting the car. It only needs a really quick shot. If the car starts right up then it must be a fuel problem. What this spray does is put fuel through the air intake and into the engine as opposed to through your fuel injectors. So if it works then fuel must not be getting through. From there, start diagnosing the fuel delivery system starting with filter, pump, injectors, etc.
Monday, September 7th, 2009 AT 5:26 PM