Playing HTML5 video can be tricky. There are 3 things to check for:
- check your MP4 files is properly encoded for web delivery. You can try to use handbrake or MP4Box or ffmpeg to repack your file. You need to activate the "web optimized" option (aka fast start) with handbrake.
- check your server config: for mime types have a look here section "MIME Types Rear Their Ugly Head". Try to restart your Apache server after the changes in config. If it does not work in .htaccess try your site-wide httpd.conf. Other things to check includes CORS and 206 Partial Content/Range Requests
- check your script/HTML5: try a barebone HTML5 video tag in a blank page with your mp4. If it works then scripts in your page may be affecting video playback. You can also check CPU load when playing back full HD videos.
I normally use videojs mp4 sample as a reference for a known working mp4/server config. This applies to mp4 but for webm/ogg as well (you can use make web video for transcoding to WebM or Ogg).
Let us know how it goes.