Part I will be mostly zeros (one or two boxes may have entries for other reasons), but you should not be making any entries directly to Part I anyway, if I understood you correctly.
You are correct in thinking that you must file the 8889 because distributions were made from the HSA. Just go through the HSA interview as normal (Deductions & Credits->Medical->HSA MSA 1099-SA), enter your 1099-SA, and make no entries for contributions.
