Magento – Magento place order redirects to shopping cart empty

First way:

1. You'll have to override app/code/core/Mage/Catalog/Block/Product/List.php block and create a new function which will load your custom form which use to insert birth day etc.
2. Then in the template file app/design/frontend/base/default/template/catalog/product/list.phtml around line 61 and line 103 invoke your custom function instead of getAddToCartUrl($_product) function in the onclick event of Add to Cart button
3. Make sure to invoke getAddToCartUrl($_product) function inside your custom function after submitting your custom form.

Second way:

1. Write an event/observer to inject your custom form when user click the Add to Cart button. You can try with this event 'checkout_cart_save_before'.

Note: I didn't test this event. If it didn't work refer here for achieve the relevant one http://www.nicksays.co.uk/magento-events-cheat-sheet-1-7/

You're editing the right file. I have a few suggestions.

1. Make sure you clear the caches every time you modify phtml files.
2. Enable Template Path Hints in System > Configuration > Developer. Change to a store view to see this field. Go back to empty cart page and you should see the right path.
3. If 2 is not an option (e.g. you're on a live site), check System > Configuration > Design. See Current Package Name and Templates fields. You have to edit app/design/frontend/[Current Package Name]/[Templates]/checkout/cart/noItems.phtml. If Templates field was empty replace it by default.

Hope it helps.