I tried to upload a GIF to a test blog and had similar results in that all I got was a static image. One solution I was able to come up with was using the template modification for adding gadgets and widgets to your blog header.
Another option you have here is instead of copying the "HTML code" from a image hosting site like Photobucket you can use the "Direct link" code they provide.
<img src="Your Direct Link Code Here" alt="">
Don't forget to back up and save your template and or try this on a test blog first.