Sounds like your headset definitely isn't installed correctly. From the bottom up, with an integrated headset it should go crown race on the fork (make sure it's all the way on, it can be hard some times), bearing in the bottom cup, bearing in the top cup, slide the fork through, slide the compression ring down over the fork until it clicks into the top bearing, then put the dust cover over that. And then obviously your compression system comes next. A brand new headset will sometimes squeeze the grease out the first time you compress it too, so it's a good idea to clean and grease your headset whenever you have to take your compression apart.