There are DVD Itentifier TOC (Table Of Contents) information that's stored on a consumer (purchased) copy that copied DVD's do not have, nor will they have. In order to play a personal DVD backup, you need a PS2 version that supports DVD-R (+R+/-RW) media. If you do, then a mod chip will trick the PS2 into thinking that you just put in a store bought PS2 game.
You also need to make 21+ solder points, depending on which PS2 version you have.
Of course, I really don't know who would go to that extent just to play their own personal backup's of games...