I have an older car with fuel injection. If it gets parked with the front end higher than the rear for any length of time, you have to crank it for at least five minutes, even if you move it to a flat place or with the rear end higher, before it'll start. When you start cranking it doesn't fire at all, then fires intermittently a pop every few revs, then gradually more and more firings until it can run on its own. (of course I don't crank for five minutes continuously or the starter would overheat.)
I'm guessing there's a slight air leak in the fuel system? Or is it something else?