The Samsung Galaxy Tab A 10.1 is known by different models depending on the features. Regular model: SM-T580 (WiFi), SM-T585 (3G,4G/LTE and WiFi) released in May 2016 or S-Pen model: SM-P580 (WiFi), SM-P585 (3G,4G/LTE and WiFi) released in September 2016. It is a 10.1- inch tablet manufactured by Samsung Electronics and their new high-end “A” series.
The screen is not working can be happened by many types of errors but what you can try is to reset your phone by doing factory reset and before doing it just take a backup of your data.
If this idea not work then just go to a mobile repairer and don’t take further risks