My car has trouble starting sometimes and it tends to put out white smoke. Got my alternator checked and replaced. Unfortunately it still has trouble starting. Could the new alternator be bad? or could it be the starter? or possibly a dead cell in battery

when you say you have trouble starting it does it turn over or do you have to boost it? you said there is white smoke coming out of the exhaust does it come out all the time because it sounds like you could have a blown head gasket which could give you starting problems?