Suddenly ALL of my notebooks are corrupt. Even the new ones I open are corrupted from the instant I open them. I've tried the notebook restore utility. Any other suggestions?
If ALL your notebooks are corrupting, that means there is something systematic about your Mathematica or the disk the notebooks are stored on.
Quick test: reset Mathematica's initialization files, in case one was damaged and is starting Mathematica in an odd state.
See http://support.wolfram.com/kb/12464 .
Another possibility is a damaged style sheet. Determining and fixing this would probably take more time than removing Mathematica and re-installing it.
I would contact Wolfram Technical Support (http://www.wolfram.com/support/contact/)
What do you see when you open your notebooks? Is there a message saying the notebook is corrupted? Are you using a network drive or saving the files locally? What OS are you using?
This information will help them better understand the problem.