Interrupted Upgrade to 4.5.1

If you have access to your files via ftp, you should be able to upgrade WordPress manually.

According to WordPress.org, you can do so by swapping out a few folders and files:

Step 1: Replace WordPress files

1. Get the latest WordPress zip (or tar.gz) file.
2. Unpack the zip file that you downloaded.
3. Deactivate plugins.
4. Delete the old wp-includes and wp-admin directories on your web host (through your FTP or shell access).
5. Using FTP or your shell access, upload the new wp-includes and wp-admin directories to your web host, in place of the previously
   deleted directories.
6. Upload the individual files from the new wp-content folder to your existing wp-content folder, overwriting existing files. Do NOT delete
   your existing wp-content folder. Do NOT delete any files or folders in
   your existing wp-content directory (except for the one being
   overwritten by new files).
7. Upload all new loose files from the root directory of the new version to your existing wordpress root directory.

Step 1.5: Remove .maintenance file

If you’re upgrading manually after a failed auto-upgrade, delete the
file .maintenance from your WordPress directory using FTP. This will
remove the “failed update” nag message.

Step 2: Update your installation

Visit your main WordPress admin page at /wp-admin. You may be asked to
login again. If a database upgrade is necessary at this point,
WordPress will detect it and give you a link to a URL like
http://example.com/wordpress/wp-admin/upgrade.php. Follow that link
and follow the instructions. This will update your database to be
compatible with the latest code. You should do this as soon as
possible after step 1.

Don’t forget to reactivate plugins!

Step 3: Do something nice for yourself

If you have caching enabled, clear the cache at this point so the
changes will go live immediately. Otherwise, visitors to your site
(including you) will continue to see the old version (until the cache
updates).

Your WordPress installation is successfully updated. That’s as simple
as we can make it without Updating WordPress Using Subversion.

Consider rewarding yourself with a blog post about the update, reading
that book or article you’ve been putting off, or simply sitting back
for a few moments and letting the world pass you by. Final Steps

Your update is now complete, so you can go in and enable your Plugins
again. If you have issues with logging in, try clearing cookies in
your browser. Troubleshooting

If anything has gone wrong, then the first thing to do is go through
all the steps in our extended upgrade instructions. That page also has
information about some of the most common problems we see.

If you run into a request for FTP credentials with trying to update WP
on a IIS server automatically, it may well be a matter of rights. Go
into the IIS Management Console, and there to the application pool of
your blog. In its advanced settings, change the Process Model Id into
LocalSystem. Then on Sites, choose your blog, right click, click on
Edit permissions and on security tab add authenticated users. That
should do it.

If you experience problems after the upgrade, you can always restore
your backup and replace the files with ones from your previous version
from the release archive.