I’ve had this problem on several of my sites upgrading to 4.3.x. If removing the .maintenance file didn’t work you may want to try checking folder and file permissions. All folders should be 755 and files 644. I had a mixture of too strict of permissions and not restrictive enough on some files. WordPress won’t install if permissions are too weak. Once I changed all the permissions the WordPress upgrade button in the dashboard worked perfectly. You can go into cpanel and use File Manager. This takes awhile and frankly doesn’t work perfectly with so many folders/files. I wasted a lot of time using it. What worked right off the bat for me on another site with same problem was to open an SSH and run these two find commands:
To change all the directories to 755 (-rwxr-xr-x):
find /yourdirectory -type d -exec chmod 755 {} \;
To change all the files to 644 (-rw-r–r–):
find /yourdirectory -type f -exec chmod 644 {} \;
