Sorry for not getting to this sooner but I wasn't on the forum yesterday. What cover are you talking about that you can't get off? Sounds like you have an air leak somewhere on the suction side. It doesn't take much of a leak to prevent the pump from priming. These pumps are not designed to pump air, only liquid. They will pull a slight vacuum then damp and virtually no vacuum when dry. Whether they prime on their own or not is determined by how much vacuum they can pull and the level of the pump above the water surface. To help it along with priming you should fill the pump basket chamber with water, seat the lid, then fire the pump. Most common source of an air leak is the pump basket lid gasket. Wipe clean the gasket and mating surface and lube the gasket with silicone grease. If you see any cracks, tears, etc on the gasket, replace it.
Hope this helps.
Al