Did you change anything before this started happening? Anything, like add an A/V receiver, mess with the cables, added an input to the DVD recorder.
If not then it sounds like (no pun intended) you have a problem with the DVD recorder. I have 2 panni DVD Recorders and both support playback of something recorded while recording something else at the same time and like you did before, I only get the playback sound.
Now on mine I have each recorder hooked both directly to the TV and to my A/V receiver as many times I don't turn on the home theater to watch say the news. But since I am hooked up that way, if my TV is selected to DVR and my A/V receiver to the Cable Box then I will hear the DVR from the TV speakers and the Cable Box channel from the home theater speakers.
I suspect something is wrong with your DVR though, I have never had it literally record both the sound from what I was playing and recording on a single recording so when I played it back both were there. I also can't imagine how you could even get it to do that if you wanted to unless everything was hooked to your A/V receiver and it has some kind of mixer function.
Sounds like it time for a trip to the repair shop. One thing you might try first is unplugging your DVD for a couple of days and then plug it back in and see if the problem goes away on its own.
Ok here is the problem Im in the Uk I have a Philips LCD tv with a freeview tuner built in and a Panasonic DVD DMR EX75 Recorder with Hard disk with built in freeview Tuner. So I Can normally record different to what im watching recored and play at the same time do time slip and such things. Normally in the past when I play back a recording and at the same time happen to be recording at the same time i would only have the playback sound now im getting sound from the playback and the recording at the same time because im obviously playing back through the EXT 1 DVD channel. Or if the DVD as been left on tuned to a receiving channel i will Have both sounds. So im now at the position where I cant record and play at the same time which is how analogue VCR's were.