There's no Mp4/H264 limitation here in WMP, which hints at the need for the necessary codec on your system.
Tools exist to find the specific codec, but folks have had luck with a codec pack - perhaps overkill, with slight potential for codec conflicts, but generally effective.
Suggest that you install the well thought of, widely used K-Lite basic codec pack. Click on the 'Mirror 1 or 2' links only.
Or simply play the file with VLC or MPC-HC. Both players handle most every format, and are free.