Hi Joanne!
I would go and correct the broken links - either replace them with active/working links, or remove them.
Since past blog posts are kind of like a library - they're always there, and people can stop by and "check them out" any time - you are already generating views with that blog post, so I would just spruce it up. You can always do a second, "update" blog post - but don't underestimate the value that that old post still has! Remember that folks visit blog posts and bookmark them and pin them to Pinterest—to return to them later on.