This happened to my S4 as well. Like most of the earlier posts I read, this occurred on Monday. I tried everything that was suggested in the posts-removed the SD card, un-synced a number of things, downloaded Wakelock Detector, and removed the battery for 30 minutes. Removing the battery helped a bit, but the next day, the battery was draining again. I started looking at what was slowest and the only thing I noted that was different from when the battery started draining - my email was taking a really long time to load. So, I deleted the email account on my phone. Then, on my laptop, I cleared out the deleted emails. Then I set up the email account on my phone, from scratch. I set it to retain only the emails for 2 weeks instead of 1 month (the default), and I have had no other issues with the battery draining. My emails load fast as lightning now and that little circle at the bottom of the screen doesn't turn endlessly. My email is not a gmail account, but it is "managed" by Google's gmail. I don't know if that makes a difference or not, but I hope this helps.