I have not seen any issue with the Powerstore being in a subdirectory of the root. I have tested this before and was able to get the store running smoothly, so that shouldn't be an issue.
The index.php in the root directory shouldn't cause any problems with the index.php in a subdirectory. Try putting in another file into the subdirectory and trying to access it directly using a similar url.
It could be a permissions error on the directory.
The page showing up as blank could also imply that there is an error occurring on the page.
Add the following code at line 1 of your page to turn on error reporting:
Then reload the page, it should show the php error that is occurring.