I had a problem with using WordPress’s Blogger import feature as well. It was bringing over the text but only the image text links and only some of the other information. Here’s what I did to import it and it worked like a charm!
1. Go to your blogger.com blog and export the blog file. (https://support.google.com/blogger/bin/answer.py?hl=en&answer=97416)
2. Go to this site:( https://blogger2wordpress.appspot.com/ ) and upload the .xml file that blogger saved to your computer. This nifty little app will translate all that blogger info into something that the newest version of WordPress (3.3.1) can actually read.
3. Go to your wordpress dashboard and selct Tools> Import> WordPress
4. choose the file that the blogger2wordpress app saved to your computer. (also a .xml but one that WP can actually understand)
5. This should link all images back to your blogger.com hosted images (so don’t delete your blogger.com blog!) all the categories, links and comments should transfer over to WP.
6. if you want to move all your images from blogger to be hosted on WP, look in the Plugins where you should be able to find several good plugins that can help you do that.
Good luck!