Okay, just to clarify for any future users who may have this problem:
If you want to put a list of recent posts using the “get_posts” tag within your sidebar, then your sidebar MUST occur AFTER your main blog content area in your PHP document. In other words, get header, then the post data, then get sidebar, then get footer. For some reason if the sidebar is called BEFORE the blog content, it interferes with the way links normally work. I always wondered why all public themes put the sidebar so far down on the page, right before the footer. Now I see that there is a good reason for it.