When restore points simply won't work when trying several you then have to start suspecting something else at work including a possible malware infection of some type. I would first try turning off the restore feature entirely to see all present points wiped and run a good security sweep of the system.
You may have only seen a bad batch of restore points that simply ended up being corrupted and unusable while this would be one idea to rule out any virus or other bug as the source. The fresh points created llater would then be totally bug free and likely to work.
The SFC tool of course would be used to verify the main files are present and in working order. It does seem to be more of an OS related problem however.
One better option you could have used when everything was working in prime condition would be the creation of a full system image backup where you can recover everything including all programs and device driver
installs from one image. Backup Complete Computer - Create an Image Backup
Once you have an image onhand and have any major "oops!" you can simply restore the image to get everything back as it was. That can be a large relief!
I'm just hoping the original 7 install the system came with saw a good install and not simply a partial with most everything but... working as it should. Surprizingly restoring a full image backup doesn't take more then 20-35min. especially when the image is made with nearly 500gb of data on the main drive as the image was about 465gb in size here for one. First you need everything working well however.