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Black screen in the middle of a game usually means a bad dump. You could try downloading them from a different source.
There are a lot of opinions on these. It's unquestioned that Verbatim/Taiyo Yuden are the top brand discs you can buy and keep your laser healthier for a longer period of time. But other people have had success using other brands. If downloading the games from a different source doesn't work, you could try different media and it might help.Get Verbatims and report back?