I couldn’t find anything unusual in Chrome or Firefox. Hoping those are now ok. I did reset Chrome again and imported nothing, save my exported bookmarks. Nothing unusual in Local Settings anywhere either. I tried to access the admin pages on the broken sites again but could not see these redirects.
The article on using Google’s DNS servers was interesting. I did switch to them because my ISP DNS servers kept playing up. Now I don’t know whether to switch back or not, maybe it would be good for a while.
I think all is likely to be ok, so now I need to look at re-installing WordPress for these sites. I have the database backed up, and have saved the config.php and the uploads folders. I don’t think I need anything else, and I checked the uploads for suspicious files, all looks clean.