I have an Asus external DVD drive that has worked well with my Surface Pro 1 but did not work at all with my Surface Pro 3. It was producing some of the same symptoms as seen in this thread. I tried a number of third party DVD player programs to no avail.
I could see the drive and the individual video files in both the Windows file structure trees and within the third party media apps, but I couldn't get the drive to keep spinning or the videos to play.
I recalled what I had done a few years back to get it working with my SP 1, which was to install Windows Media Center as my default video player. This used to come bundled with Windows but MS carved it out and now charges approximately $10 for the "added
feature". It does have the virtue of "fixing" my external drive, so that after installing Windows Media Center, videos play without issue. If anyone's willing to risk the expense, here's a link explaining how to add features to Windows 8.1, in this case
"Windows Media Center": http://windows.microsoft.com/en-US/windows-8/feature-packs
I laid out a beautiful dollar and then some to get the absolute high-end SP3, but I didn't get this simple capability, which is irritating.