My advice: Keep buying crap.
I have gone through two really high end dvd players (One, an $800 mitsubishi and the other a $1,500 Sony) and both started out fine, but after a year or two, each one started having problems. And yes, I too have a little one that loves to watch movies. (After she goes to bed for the night, then we watch our dvds too!)
I learned my lesson and started buying cheap dvd players. They seem to last just about as long and the picture quality is decent, but maybe not quite as good.
(But for me, that is fine, as I am ambivelent about video.
Music and my 2 channel is my passion.)
My two cents worth.