I would suggest that you re-upload / reinstall Wordpress - seems that there are files missing from the installation, or that there is some sort of redirect that isn't happening, or maybe your .htaccess is just messed up (although the /wp-login.php should still work).
Looks like a misconfigured server of files. better contact your hosting provider and let them to fix the things for you.
Its better if you ask your host to debug the problem for you, usually they will be able to help you sort this out or if you want me to help you get this sorted then let me know.
Usually a fresh/re-installation should work, but I've had to ring my host a few times when a new installation didn't help - they will sort it out for you.
As per 404 error it seems the folder is not present or there is error with permission or ownership of the file. Seeems pretty simple for your hosting provider, ask them they should get this fixed for you.
download again new wordpress files manually from wordpress.org and extract (overwrite) the old files, seem you failed when last extract so some files not included