Why can my Macbook plays sound in Windows but not OS X?
So with a lot of time and hard work on behalf of a much more patient friend of mine, I was able to get the stuck piece of headphone out of my Macbook. I can now use my speakers, however the headphone port itself is not working. (There may have been some super glue in it from when I previously tried to remove the piece, and it required a lot of digging and scraping to get it out)

Unfortunately this does not answer the original question I asked, but it would appear that there is absolutely no way to make OS X play sound, even though Windows has no issue playing sound. This is very unfortunate. Good luck to everyone who was in my situation, and thank you to everyone who posted their advice in the comments. I appreciate it! :)