"We could not complete your purchase" dialog on login
If you open Mac Store and under your Apple ID you will see all the items under Purchased (Application such as Keynote, Pages, GarageBand so on). So even it is free, it is counted and listed under purchased items with zero cost/charge. 

In your case, I think your machine is trying to download some updates from Mac Store for your application that you have downloaded from store and it is unable to do as you don't have enough space for its upgrade. Make some space free first :)