There's nothing wrong with the PNG format, assuming you're not using IE6. (And if you are, please for the love of God, upgrade!)
Mostly likely the web server is looking for an authentication cookie before displaying the images-- i.e. you have to be logged-on to Blogspot to see them. It might also be checking referrers-- i.e. the site trying to load the images needs to be Blogspot. Or the URLs could be caching URLs-- i.e. the URLs are only temporary and not guaranteed to work permanently.