First of all, it looks like you moved your Wordpress site from localhost to the live domain, and that's why the site doesn't work and appears to be without styling. You need to take a look at See Moving WordPress « WordPress Codexand WordPress Serialized PHP Search Replace Tool to move the site correctly so it works.
And when you're ready to move it to the main folder, look at Giving WordPress Its Own Directory « Using a pre-existing subdirectory install
If I could figure out how to get to the HTML files then I could maybe do something, but I can't find any
There are no html files; all content is in the database. There are theme files you can edit to change the twentythirteen design, but if you do that, make a child theme; see Child Themes « WordPress Codex