You're unlikely to find spares listed for a small, cheap player like that. Your best bet is to see if you can find a push latch of the right size, shape and fixing on any of the tat bazaars like eBay, Amazon, Banggood, AliExpress, Dealextreme, etc. It's a lot of legwork.
Why not just rip your DVDs to mp4 videos, pop a large memory card in your phone and watch on that? If it's for your kids, give them an old phone with apps you don't want them to use, hidden away.
Ekdj
November 2022