I had that problem on a two year old Panasonic RP-56. At first it helped if I unplugged the unit for half an hour, but eventually it stopped responding to all button presses after the DVD was inside the player and was being loaded. It was a great player when it was operational, but rather than spend money to fix it, I just bought the HD-931 to have full 720p upconversion.
Now, about six months later, I own the Denon 2910 because of the lip sync problem on the 931 (but that's for another thread). I've only had the 2910 a day, but my initial impression is that it outperforms the 931 by a wide margin on audio, and to a lesser (but still noticeable) extent it outperforms on video as well.
Don't know how to fix your problem, but it sounds like you now have the perfect excuse to upgrade your DVD player!
Good luck...
-Corey