So I've just did a clean install of 3.8 on the new server. I updated the old install to 3.8 and updated all the plugs as well to ensure compatibility of the data.
I just copied the wp-content folder over and imported the old database. So far, it looks like the site is working.
The problem is that I can't log in! I noticed that the new wp-config has these authentication keys, whereas my original install wp-config did not. I figured that just removing these from the new one would solve it, but it didn't.
Any idea what else could be preventing log in or what would need to be changed in the new install?