If the cages are in deplorable condition you must report the situation to the local Animal Shelter - usually the SPCA. Before you make a report be certain that you are correct because the next time (if they find nothing actionable the first time) they will be VERY reluctant to check. As far as socializing or playing with the animals I am not aware that any pet stores do that. Unfortunate but true - they are in business to make money and that involves spending as little on overhead as possible.
Have you applied to any of the private animal rescue organizations in your area? When I was active in animal rescue a number of people, 12 and up, were very active in caring for the animals, walking them, socializing them.