Say I take short audio clips from various TV shows and bundle them up into an application, would it be considered fair use or is that not allowed under copyright law or some other law? The final product will in no way resemble the original. (I am not going to be taking clips from a show to reassemble them back into the show. It will be something completely different.)
Is it still legal to make money off this?
I think it's incorrect to assert that the final product "will in no way resemble the original". The final product resembles the original in that each snippet looks like the portion of the original from which it came. If the final product actually "in no way" resembles the original, then you are definitely not infringing copyright and no fair use analysis is necessary.
There is no way for us to know whether the use you describe is fair use. Fair use is determined by a four-factor balancing test (17 USC §107). Whether you are selling the work factors into the test, but it is not determinative.
Stanford has compiled a bunch of examples of successful and unsuccessful fair use defences. One that seems somewhat analogous to yours is Cariou v. Prince, No. 11-1197 (2d Cir. 2013). In that case an artist, Richard Prince, took images from a photographers book and made a collage. The court found Prince's use to be fair use.
