If someone does a study which, for statistical reasons, I think is hopelessly underpowered or nonidentified, my best and most useful advice will not be tips on how to calculate p-values better, or how to construct an explanation for some particular data pattern. Rather, my advice will be to start over, to reconsider what you think you already know, maybe to question some prominent work in your subfield, and quite possibly to think a lot harder about measurement, and about the relation of your data to your underlying constructs of interest.