I've got an ancient Pioneer that is the only DVD player I've ever had that plays any kind of original or copied DVD I put in it. It does have discrete ON/Offs. I suggest looking at the newer Pioneer DVD players, although I've not prersonally bought one. Of these that I have, only the APEX and the Panasonic seem capable of reading most of what I put in them.

Samsung DVD-Recorder with NTSC tuner: Won't play most original DVDs, but does play every copy I've put in it.
Cyberhome DVD with 1080 upscaling: Piece of junk.
Truetech DVD/HT_in_a_box: Seems to work, but has manual POWER button. Real pain.
APEX DVD: So far reads everything. Using it as a music player to feed outdoor speakers. Will read MP3s off a DVD, and will randomize playback.
Panasonic DVD recorder with ATSC/NTSC tuner: So far plays all I've put in it. Tunes and records digital OTA channels.
Pioneer DVD: Most expensive and most reliable. Very old tank. I know it has discrete ON and OFF, as I use them with my universal remote.