My Honda Civic starts up sluggish

I would suggest that you look at the fuel system. Now there is couple of things to look at. First off, I would start with the fuel injectors. I am thinking that there is an injecter that though it works fine in the operation of the car engine while running, it leaks while sitting for a longer period of time. When the car tries to start, the pressure in the system is lost and must be repressurized. When you turn on the key, does the fuel pump seem to run for awhile? Try this. Turn the key to the position right before the engine starts to turn over. Let the car sit for about 10 to 15 seconds and then give it a try.

You replaced the rail and was that with the injectors as well? In other words, did that give you different injectors?

Take off the EGR valve and clean it. Put it back on but you may have to get a new gasket for it.