The hell as a negation in the affirmative (an affirmative statement of negative sentiment, a non-negative negative.):
John Lawler covered most of the common uses of "the hell" and its variants in his linked article. I would add one other use that might be applicable to your examples.
"The hell" is sometimes used to negate a statement while at the same time providing emphasis or intensification. A statement may sound as if it is affirming a fact, but it is actually stating a negative. The hell I will means "I will not".
Note that there is no other form of negation used with "the hell" in this case. This differs from the examples that John Lawler and Hellion gave. (There is nothing wrong with their examples, mind you.) So "the hell" supplies the negation all by itself.
This use of "the hell" is actually short for "the hell if", as the following example shows:
Let's look, in this case, at your example. To say "You cannot do anything (to me)" might be a reaction to someone suggesting they can do something. Another way to put this might be something like The hell if you can do anything (to me).
Here you can see that the negating phrase is "the hell if" rather than just "the hell". You can substitute this more complete version in my earlier example, yielding "The hell if I will", where it works just as well. Leaving "if" out sometimes works and sometimes doesn't work.
A more complete verbal exchange along the same line as your example might be something like I can (verb) you for that!. An appropriate response might be The hell you can! meaning "You can't do that". Or The hell if you can do anything about it. meaning "You can't do anything about it."