No. Neville Longbottom's parents are not dead. They were tortured with the Cruciatus Curse by Rodolphus Lestrange, his brother Rabastan Lestrange, his wife Bellatrix Lestrange and Barty Crouch Jr. After this incident they lost their sanity due to the intensity of the torture and were shifted to St Mungo's Hospital for Magical Maladies. They remained there for the rest of their lives as they were incapable of leading a normal life after this accident. Neville visited them regularly along with his grandmother Augusta Longbottom.