A Cook County jury awarded more than $2.5 million to a man after part of a door to his apartment fell on top of his head, causing lasting pain.The verdict came Tuesday for Sean Casey, 31, who was struck by a hydraulic door closer mounted to the top of the doorway as he was returning from an early-morning dog walk in January 2009.Casey sued property manager TLC Management Co. for failure to maintain the building — despite having an on-site manager whose daily tasks included ensuring its maintenance and safety.As Casey …