"Page not Found" after seemingly successful manual Core Update

Hello all:

I've recently tried to get back into developing Drupal sites after a brief hiatus but I keep having the same issue with trying to manually update Drupal Core past the 7.22 that I was able to install automatically via my GoDaddy hosting.

With a clean install of 7.22 (no additional modules, nodes, content, etc.) I try to follow the update instructions (put the site into maintenance mode, delete everything except the sites folder, copy over everything except sites from the new core) I then navigate to update.php and proceed, getting no errors. The main page seems to load fine, however clicking the link to take my site out of maintenance mode returns a "Page not found" error and so does every other link. This happened when I tried updating to 2.6, 2.7, and even 2.3, and I'm feeling quite stumped.

I am attempting all of this is a subdirectory of a root that also has a separate Drupal instance/server installed, but I'm not sure if this would affect anything.

Any help here would be greatly appreciated.
Apologies if this is duplicated elsewhere in support; I was seeing a lot of instances of update.php being not found, but not of everything else after update.php seemed to work successfully.

Thanks,
Stephen