Thanks to all who replied. The disks I've tried are just popular movie DVDs that my son checks out of the library. Many movies work fine; every time I've had a movie fail to play properly, it turns out to be a DL disk.
I did contact Funai support, but they are the ones who referred me to Sears, saying that I need an upgrade, but that they can't help because this player is a model produced for Sears. Sears support hasn't replied to my emails, so I'll try calling their local repair center & see if I get anywhere.
Thanks again chef, pinto2 & tehGrue.