Im sorry I dont know any specifics, but a next step would be two things: Have a look at the plugs, to see if they are clean and white, or if one or more of them is dark, dirty, or even wet. If you had the old plugs it would be a good idea to look at them too.
Then, do a compression check. Low compression for whatever reason can lead to a plug running cold and not firing reliably when everything is cold. If the compression is good in all cylinders, my next suspect would be either poor fuel pressure in the fuel rail (hopefully there will be a fitting to check it somewhere on that fuel rail) or an injector that is partly clogged - or even not shutting off (which lets fuel leak into the cylinder it feeds, causing a too rich condition). I dont own a Cavalier, so these are the kind of things that can happen to any car with individual injectors.