From Magento 126.96.36.199 there is a feature called Blocks Permission that allows the defined block can be display in CMS page / CMS static blocks.
If you don't see the Product slider display correctly in CMS page, then look at the System > Permissions > Blocks
If there is no block called productslider/productslider or similar that name, so you have to add it into this grid.
Click on Add new block > Fill as the following:
then click save.
Now go to frontend and see the changes.
If you have any problem, feel free to create a topic