I have a website built with bootstrap and loading video in a dialog:
First check your web page here for test
http://html5test.com/
Second inspect via code inspector and enter them in the browser to check if the are working fine or not. Or drag and drop video file over the browser to check if its working or not.
Thirdly try checking MIME Types
AddType video/mp4 for .mp4 .m4v
AddType video/ogg for .ogv
AddType video/webm for .webm
Fourthly check you html5 converter it has often problem with format conversion I had same problem year back when I was working html5 video. Changing it fixed the issue for me.
Last but not the least; Add a flash fall-back!