I had the exact same problem, posts were all there and could use the “Entries” link at bottom of page to scroll to the posts, but links on Calendar and Archives wouldn’t work. I had a custom permalinks setup also. Reset Permalinks to default settings and the problem is fixed. I am using NO plugins and am using the WordPreess Default theme with only a couple of custom settings.
Not a big deal for me at this time, but it was a bit disconcerting.