The title pretty much says it all, but to make things worse, new files aren't tracked as well. I figured that this is likely a rare exception, but it would be good to know what is causing the issue - in case a large project gets bugged by it. This question might help anyone who gets in this mess, so please post your suggestions.
Here is a screenshot of the situation: https://i.sstatic.net/iMn3O.png
Here is the screenshot I posted of the Settings... > Version Control > Ignored Files page: https://i.sstatic.net/9F0sq.png It shows what is wrong on the 3rd line.
If you still can't index:
It might be because after removing the ignoring of your files, that the VCS hasn't been brought up to speed of the fact. Go to VCS > Show Changes View and then hit CTRL+F5 or click the Refresh Icon. Now you have Unversioned Files and you're ready to add files to the index.
I have solved the issue with a roundabout way. What I did was: I didn't include the .classpath file that Eclipse creates. IntellIJ asked if I wanted to open .project, I canceled that and just opened the project regularly, that solved it for me. It might have quietly induced the ignore entry from the screenshot.