If you've tried several adapters and none of them work, assuming that they're reasonably close to 9v->12v @ 850mA, then you have something wrong internal to the NES. Sounds like something in the rectification / regulation stage, like a bad diode bridge, main filter cap, or 7805 regulator.

You mentioned that you tried a few DC supplies - are they all of the same polarity? If so, try to find one of the opposite polarity and see if it makes a difference.