Plugins trying to upload to the media uploads folder

A client’s website has gone haywire. One of the problems is that when you try to upload a plugin using the dashboard Add New feature, it tries to put is in the media library uploads folder. In the past, it has succeeded in doing so (but then won’t activate). Now it just throws an error page that says:

The uploaded file could not be moved to wp-content/uploads.

At the same time this happened, all the thumbnails in the media library changed from the images to a generic gray icon. Have deactivated all plugins, change permissions, about anything I could find in the forums. (These images were NOT created or uploaded using a plugin, per some threads.)

Ideas?