you can't play burned games on any ps2 except if you modify it, or use swap magic.
that's not true there is a hack somewhere that you can install on the memory card but i don't know how that's done or how it works i just go and buy the games in the shop
(you will need a 32mb card as the hack uses 17.9mb)
also i would like to add that modifying the console in such a way is first highly illegal and 2nd will expire any warranty and right for customer support that you may have and this can majorly damage the console so i would recommend just buying the games in store.