There is a problem in New.php block, which goes with default Magento package.
form_key field is set not properly when cache is enabled. Therefore there is no way to add a product via New products block.
Detailed description with a solution: Magento add to cart issue on caching new products
In order to fix the problem cache_lifetime="1" line should be added.
For example, replace the code
with the code
Flush the cache after you apply the fix.