When it comes to “publishing” your work on the internet, either though blogging or sites like CTRStories, do you need to let a prospective publisher know that it’s been on the internet? For example, if I blog about my child with dyslexia and later decide to write a book about dyslexia using some of what I’ve written on my blog, will that cause a problem?Yes, you do need to let the publisher know. Let's say you blog regularly about dyslexia and people come to your blog specifically because of that, then you've already begun to establish yourself as an authority in this area. That is a good thing.
Whether or not it causes a problem depends on how close a match the two pieces of writing are. If what you've posted is word for word what is in your book, you're going to need to take those posts down before you start submitting. You might leave up a small number of posts (ones that have the most positive comments) to show that people respond well to your writing but if you have too much up there, you're diluting the sales potential of the book. It's a fine line—you want enough there to entice people to buy the book, but not so much that they feel they've already read it.
It also depends on the publisher. Some have a policy of no excerpts posted anywhere. Others feel that a few short excerpts are a good thing. Even those who are very strict will probably not have a problem if what you've posted represents just a few pages of a much longer finished work, but they may have you take it down when they offer a contract.
Personally, I would not post anything I was planning to publish in print on the Internet until I had a signed contract with a publisher and their permission to do so.