Maybe this will work?

I went surfing through the blogger help forums looking for something about the problems with inserting images. If you get the pop-up that shows already uploaded Picasso images and doesn't seem to have a way to upload from your computer, look for this button.

I never noticed it and now I keep seeing the familiar pop-up with the option to upload from the computer, so I can't confirm that it will work.

As someone who has made a living designing user interfaces and testing usability, it doesn't seem at all intuitive to me.  But as with many non-intuitive things in life, I suppose we can all learn it and move on from there.