404 errors in admin- especially plugin settings

I had to restore from a backup due to a hack attack about ta week ago. I thought everything was fine until I tried to change some settings in a plugin- I got a 404 error. I poked around and found that several of my plugins led to 404’s when trying to save a setting or even a simple deactivation.

Does this mean something is fundamentally wrong with my WP install? How can I troubleshoot this? More importantly: how can I FIX this?

[No bumping, thank you.]