It could be any of a number of problems: starter, keyswitch, fuel pump, any of a number of electronic devices could be responding to a heat condition...
In general, if it isn't the starter start with a computer diagnostic. You can borrow, rent or buy a code scanner at most auto parts retailers.
Figuring out what the cause of the problem is would be the place to start.
Would this cause the car not to start If the EGR VALVE is bad
One cause would be a cold spark which means you have either a loose coil wire or a bad coil.
Bad EGR valve
probably the starter
i would change the electrical part of your ignition switch- i would change the electrical part of your ignition switch-
check the ignition modulator under the distributor cap
Blown fuse, or defective headlight bulb.
Try changing the oils the relate to the spudder and idle. Then try and time it.
lower intake gasket
the steering wheel..
blah blah blah if you ask this question you are a nerd