This sounded very much like a caching problem. Specifically Browser Caching.
Sometimes your Server may fail to fully serve an asset. Sometimes your Browser may incorrectly store an asset. This could have been a corrupt JavaScript file, or a corrupt CSS file. Either way, it was causing aesthetic problems on the Administration Screen of WordPress
Knowing that WordPress core, and subsequently Administration Screens should not really be modified ever, there were two options immediately available. Either you were experiencing a bad cache or your WordPress install had “gone bad”.
Caching was just more likely.
But it sounds like you needed to re-install WordPress.
That’s odd.
What probably happened is that you recently updated and the update went bad. This can happen because of not upgrading plugins first, or sometimes it happens because they do a bad release (that does happen).
Looks like the solution was to re-install.