EGR shouldn't keep it from starting. It would cause a rough idle and maybe a stall at idle.
What you've got to do is the next time it won't start is see if it will start with a little gas or starter fluid in the throttle body (careful, and it won't run long on it). And you need to see if you've got spark at the plugs. those tests would narrow down where you go next.
What you've got to do is the next time it won't start is see if it will start with a little gas or starter fluid in the throttle body (careful, and it won't run long on it). And you need to see if you've got spark at the plugs. those tests would narrow down where you go next.