loop-page.php is the wrong context for what you are trying to do.
If you want it to appear on the home page, then you need to edit loop.php, so in your child theme you can either create a file called,
loop.php
…which should take precedence over the loop.php found in the parent TwentyTen theme or better yet create a file called,
loop-index.php
…which will take first priority over the above. By doing this and NOT creating a loop.php we will allow the loop.php file in the parent theme to act as a fall back in case something goes wrong.
Hopefully that makes sense.
In summary, you want to create a loop-index.php file (best option).
You can simply copy the contents of what you find in loop-page.php over to this loop-index.php file to give you the basic framework for your template, then you can modify the template to your liking.