When you turn the key, for how long does the fuel pump run? If it's only 2 or so seconds, the problem isn't likely the pump.I have a 2005 Elise and as of lately when the car is cold, I have to crank it two or three times before it actually starts. If I just try leaving it cranking on the first try for 10 seconds or more it still won't start, but if i try cranking it for a second or two, then stop, then another second or two, then usually by the 2nd or 3rd try it will start.
Car runs without any issues once started, doesn't sputter / stall at all. When warm the car starts right away, and also will start right away when cold I've started the car within the past day.
With other cars in the past when I've seen this problem it's usually fuel pump / fuel pump seal related since the car isn't holding / building up enough pressure in the lines when cold to start the car right away. Could it be a similar issue with this car?
Battery is strong and the starter itself sounds fine. Car is supercharged with a REV300 supercharger, fuel pump is still stock.
Might be a good excuse to swap out to a Walbro 255 fuel pump. Is the stock pump even strong enough to reliably supply the pressure for a REV300 with the bigger injectors at the top end of the RPM band?
Check the ground between engine and chassis and clean if necessary.