Re: Can't download anything or update apps on droid turbo
Welcome to Android Central! Does this happen on both wi-fi and mobile data?
Try going to Settings>Apps>All, select Google Play Store, and Clear Cache/Clear Data, then Force Stop. Do the same for Download Manager. Now try again.
If that doesn't work, try going to Settings>Accounts-Google, select your Google account, and remove it completely from the phone. Then add it back again, and see if that helps.