I looked on some other Blogger blogs and tried their permalinks. I got mixed results; some worked and others didn't. I looked on Blogger Forum and found that others were having the same problem. Dew's permalinks worked, so I decided to ask him. He gave me a simple overview of how permalinks work, but I was still missing something. After examining my template code I figured out what the problem was.
Titles. Blogger permalinks use titles as an anchor to link back to posts. That's why a link to an old post went directly to the title of the post. I was creating my own titles using the <h4> tag, others whose permalinks didn't work were using the <strong> tag. To make Blogger permalinks work I needed to create a title that would be recognized by Blogger. Following these simple instructions made my permalinks work.
"To enable titles, go to the Settings | Formatting tab. Scroll down to the settings field labeled 'Show title field', and set it to "Yes."
"When you finish selecting 'Yes' from the drop-down menu, click on the 'Save Changes' button at the bottom of the page. Once saved, you will see a prompt diplayed that reads "Your changes have been saved." in orange at the top of the page. Do not leave this page until you see the message displayed."
After about an hour and a half I had fixed every post I had ever made, and now my permalinks work.