krakenexe on "Fatal Error - WP_Widget not found"

I'm trying to manage a site for a company I started working for last week, we run a lot of wordpress installations off a single server. We're currently experiencing an issue where we get
Fatal error: Class 'WP_Widget' not found in /home/intaglio/public_html/wp-includes/widgets/class-wp-widget-pages.php on line 17
Thrown at us on ever single page. I tried manually updating by deleting and adding the newest version of wp-admin, and wp-includes, and updating the contents without erasing the folder in wp-content.
I've tried disabling all of the plugins by renaming the plugins folder plugins.hold, and I've even tried renaming the themes that were currently active, with no affect on anything.

I'm at the end of my witts here, and appreciate any and all help you guys are able to provie, I'm quite a wordpress nooby but I feel like the steps I took should have fixed it.

For other documentations we have a second developer who is somewhat lazy and doesn't keep backups so restoring backups is a no go, and I called the hosting company and they have no backups. I haven't been able to reach out to him however, so there has been no help due to management. Also to note you can't access the wp-admin page.

Here's the website for those of you out there that feel that you need the live example
ltyc.org