I turn into a mindless zombie when I try to draw
Well, I think that might be your problem right there! (lol)
Seriously though, there's a kinesthetic side to drawing; i.e. "If I draw tons my marks will become more and more accurate," but there's also a mental side to it; i.e. "If I increase my understanding I'll know what I need to draw."
What you want to do is create an understanding of your subject so that you use your mind to actively figure out what shapes, textures, etc. need to be drawn instead of redoing your strokes over and over again until one happens to turn out right. I think Blackmage put it a bit harshly, but the thing he did get right about software is that it can tend to act like a crutch and gloss over your mistakes.
Ultimately, it's your mind that you draw with, not any specific body part. I suggest buying a drawing lesson book like Keys to Drawing
so that by doing these exercises you can learn the elements of observation, and then plunge into the basics of perspective, light and shadow, sighting and proportion, etc.
Another thing. Lots of us are by nature perfectionists. I used to erase tons on my drawings, but I've gone for at least a year without using an eraser on a single one. Don't worry about whether your end product looks bad to your own standards or not - your goal is the active process
of drawing, which you should be proud of whenever you improve.