Check out wikipedia for a good definition of warez. There are a few ways to run Linux on the PS2 - an official kit actually exists to do so. PS2 Linux is open source, available on sourceforge.net thanks to Mega Man.
As for folding at home, unfortunately the source code is not released for it, and no binaries compiled specifically for the PS2 architecture (mipsel special) seem to exist (from my quick examination), so you probably will not be able to do this. Additionally, Folding at Home is no longer supported on the PS3 as of the October 2012 firmware update, and the PS2 is much less powerful than the PS3, so there would be less technical impetus for them to compile a version for the PS2 unless you could prove that a considerable number of people would use their PS2's to help the project.
Regardless of whether it will work with Folding at Home, please check out PS2-Linux using the LiveDVD. You might find another use for your PS2 yet ;-)
PS2 v9 NTSC, PS2 v12 NTSC, PS2 v15 VESA