For me, the second link works in IE7, IE8, but not IE9 and 10 (which is weird).
Anyway, it's almost certainly a server configuration issue, as if I download the video to my PC and include it in the web page from there, it works fine in IE9 and IE10:
var BV = new $.BigVideo();
So, what to do:
Try creating a plain text file, name it ".htaccess" and using your editor of choice, enter the following:
#Video MIME Types:
AddType video/m4v .m4v
AddType video/ogg .ogv
AddType video/mp4 .mp4
AddType video/webm .webm
Save it, then upload it to the root directory of your website.
You might have some difficulty saving a file that begins with a dot on a Windows box. If so, call it htaccess.txt, upload it to the server and rename it there.
Does doing that make a difference?