For those who may have this issue also:
If you try to do searches using your default search box and doing so redirects to your homepage with no search being performed
When you click on an archive link and it redirects to your homepage without showing the archive content
If you happen to have the Robots Meta plugin by Yoast, this is the culprit causing the problem.
Here is the section of the Robots Meta plugin causing the problem: Uncheck the three BOLD settings to fix this.
Disable the author archives
If you're running a one author blog, the author archive will always look exactly the same as your homepage. And even though you may not link to it, others might, to do you harm. Disabling them here will make sure any link to those archives will be 301 redirected to the blog homepage.
Disable the date-based archives
For the date based archives, the same applies: they probably look a lot like your homepage, and could thus be seen as duplicate content.
Redirect search results pages when referrer is external
Redirect people coming to a search page on your site from elsewhere to your homepage, prevents people from linking to search results on your site.
NOTE: I have no idea why these three settings would cause the two problems I mentioned. The description for the settings mentions it's to block people outside of your website from linking to these search pages - I understand that part but why it actually prevents you from doing searches within the site itself or clicking on archive links from within the site itself I have no clue.
But anyhow I disabled these three settings and I'm back to normal with links and searches working.