Let's try and fix things with a "down to the metal" manual re-install of your WordPress site.
1) First make a backup of your files and database. Often your server control panel will have a way to manage this. Contact your host if you have questions.
2) Copy your WordPress uploads folder (this is found in the wp-content directory inside of your WordPress site on the server) to your root directory - this is just temporary and we'll move it back in just a bit.
3) Delete all the WordPress files (except wp-config.php and your just copied uploads folder) off your server - yes, themes and plugins.
4) Download the latest version of WordPress.
5) Unzip it.
6) Upload this new version up to your server.
7) Move your copied uploads folder back into the wp-content folder
8) You should now be able to login to your WordPress site.
9) Carefully install and enable your custom theme. Test and confirm everything works. If not, contact the theme developer for support.
10) Carefully install and enable plugins, one at a time. Test your site after enabling a plugin. Does everything work? If not, note which plugin you last installed and enabled and contact the plugin developer for support.
At the end of this, you should have a working WordPress site.
If you're still experiencing issues after all this, let us know and please provide details about your server setup so we can try and recreate the issue.