NIN actually always experiments with connecting things the "wrong" way
And BTW, many of his sounds aren't really digital, they are result of hooking up all kinds of guitar stomboxes, amps, whatever effects he can get his hands on... and just going with it. So... the key to creating these kinds of sounds is:
1. Open up your mind
2. Let your imagination soar free
3. Play your effects boxes/plugns like instruments
4. Sample, mess with it, resample, mess with it, resample, mess with it... resample.... ad infinitum
5. Extreme timestretching
6. Extreme pitchshifting
7. Granular deconstruction/reconstruction (Absynth, MelOHMan, Kontakt, Reaktor, MAX/MSP, Kyma and many more products have this kind of capabilities).
8. Synth layering
9. Recording nature sounds, then processing them via whatever.
10. You think that requires hard work and is extremely time consuming? You betcha!
BTW a lot of time what you percieve as some distorted sounds is not really distorted in the "traditional" sence in that it's not really distorted in a guitar distortion pedal or cranking up an amp or overloading the inputs of a mixer way... they are mutilated by other means.