- Go to Window -> New Window. This will open a second instance of Eclipse.
- Notice you can now open files again. But you aren't done - you need Eclipse to remember this setting.
- Close the old window (the one you couldn't open files with) first.
- Now close the new window (the one you can open files with). This will persist your new setting (where you want to be able to open files!).
- Open Eclipse - you should be back in business.
Hope this helps someone :-)