most efi systems these days work this way: when you turn the key to the 'on' position, the fuel pump runs for 2 or 3 seconds to charge the lines (there shouldn't be all that much pressure loss anyways)
cycle the key 'on' 'off' 'on' 'off' 'on' 'off' 'on' 'start' and see if the car starts. this is a typical neon problem, well, dodge problem. the check valve in the pump goes bad and all the pressure is lost (usually overnight), so the pump has to restore pressure first (can't start without at least 30psi) and it can't restore a totally depressurized system in only 2 seconds.
depending on what it's worth to you, it might cost a very expensive fuel pump. or don't even worry about it and just remember to cycle the key a few times to get the pressure back up.