We generally advise people to use third party programs rather than the built in burning options within Windows. And we usually try to steer people to ImgBurn, which is a free burning program. I believe it is the most comprehensive burning program available.
Having said that, it is not very popular with those who prefer simple interfaces. Drag and drop does work if you navigate to the place on the hard drive where you have the files you want to burn, then drag them into the main window of ImgBurn.
To get back to your preferred method of burning, you might try a restore point that was made prior to when you started having issues with the built-in burning options in Windows.