Generally speaking, the PS2 hardware is made in such a way as to refuse to play any backed up DVDs. This is part of the design to keep people from playing bootlegged games.
I personally think it's a bit of a ham-fisted approach - obviously it stops folks like you from playing legitimate burned DVDs on the PS2.
Maybe, just maybe, "booktyping" the DVD as "DVD-ROM" (instead of "DVD-R" or "DVD+R") when burning will trick the PS2 into playing it.
I personally wouldn't recommend chipping the PS2 as this would void your warranty and could irreparably damage the system.
Ah, well, in light of what tehGrue says I guess I'm wrong. This does however greatly improve the chances that my booktyping suggestion will work.