I found this article that says the max file size is 100 MB and that supported formats are .mp4, .wmv and .mov. My file is 7.1MB and .mov, so I'm good there.
I experience the same behavior in Chrome and IE. So I made sure I had a default video player set up on my computer and verified the video is playable outside of Blogger but that didn't help either.
So I'm just going to post a silly, short, video and hope that it's view-able after publishing. I'll be doing my own tests, but if you don't mind letting me know if you can watch the video and what browser/version you are using.
Here it is... Miles Being Silly. 20 seconds.
Of course, this one played in preview mode. hmmm.