Two problems in the Prestashop 1.5 version that messes up your head is the Free shipping appearing on shopping cart and No carrier available to deliver to this address on checkout.
Lets address them here.
1. Free shipping on shopping cart even if your shipping and carriers are configured correctly:
Make sure you have actually configured the weight and prize ranges , carriers, and had made sure you have not allowed free shipping . You may wish to make sure you have not altered the zones. In this regard we mean that you have not tried to add a new Zone other from the default Zones.
Lets say you added a new zone, assigned a carrier to that zone and then changed your preferred country(s) to that zone. This may alter your whole settings. Leaving the zones as they are and then in the carriers just indicate somehow to which countries it may benefit. Changing the country(s) to the custom zone may cause problems.
2. No carriers available to deliver to this address:
Make sure your carrier is well configures and the weight or price ranges are set within the range applied to the products. Are all your countries enabled? are your carriers pointing to the right zones?. Usually if everything is ok, once step 1 above is fixed, you should also see the step 2 as fixed.