I had the same problem last week. After few days I noticed the issue was only happening to my (gmail) personal account. My work account (also gmail) worked without any issue.

I solved it by accessing gmail with labs deactivated. Simply follow this link: https://mail.google.com/mail/u/0/?labs=0

(You can find it in Gmail > settings > labs).

After that check if drag and drop works. To enable labs again, remove the "labs=0" from the address bar and reload the page again.