It's doing the same thing for me. I'm not getting any style but the style sheets are available at the paths in the HTML. Odd.
Can you try something horrible just as a test? It'll be a temporary thing.
Try changing your child template so that there is nothing below the import line.
Edit: Of course backup the original file first.
Theme Name: Simplepress Child
Description: Child theme for the Simplepress theme
Author: Your name here
/* Get rid of all lines blow here */
Clear your cache and cookies and revisit the site.
I just want to see if it's your CSS or if the parent theme is somehow messing with the CSS. That basic child theme
style.css file should work. If it doesn't then it's the parent theme somehow messing with you (I think).