Hard cold starts can be just about anything . Lets start with engine codes is the mil light on and if so what code is it casting ? if there's no code move on to easy things like fuel filter replacements air filter, pcv valve check plugs and wires . are the plugs fouled . They should be a nice shade of ash grey . if there black or wet this is an issue. Check the pressure on the rail . As I'm not sure of the engine so I cant speak to the exact pressure . How hot or cold an area do you live in , temperature can have cause and effect as well. If the pressure is off then you may need either a fuel regulator or fuel pump . If there are codes then knowing will help narrow it down . It could be map or maf sensors or o2 . these control the fuel mix and if its off it make a hard start . There could also be a fuel line leak . Look for puddles of fuel under the car or the smell of fuel when starting . When the car does start is the idle even or does it fluctuate up and down . If so it could have a vacuum leak . Just some things to look at but start by getting engine codes read . Hope this helps