This is a rather a long answer but I hope it's instructive for thinking about similar problems in the future. Independence sounds like an absolute term but it's not. Whether samples are independent or not is relative. If what you're trying to get at is what I think it is, then yes, you can use independent measurement tests (I'm guessing by "conditions" you meant what is commonly called "trials). It's how case studies are done in performance work.
The trials are independent samples of that subject's performance. Just as the samples across people are independent samples of human's performance. While the former are correlated by virtue of being from one subject, the latter are all correlated by virtue of being measures of the same species, or same set of undergraduate students, etc. So, there's rarely (never?) any such thing as complete independence of samples. They need to be independent across the domain of generalization. If your domain of generalization is only the performance of your subject then the individual trials are independent measures.
To make it more concrete, consider your most basic statistics example; is this coin fair? Each flip of the coin is independent of the next flip as a sample of the coin. You can use them, and nothing else, to test if the coin is fair. However, you cannot use those samples alone to test if coins from a batch are fair, or coins from a mint are fair, or coins flipped by people in general are fair (assuming you made all of the initial flips yourself). They are not independent across those parameters.