When you bought the used Star Ocean: Til the End of Time game, what was the condition of the game? If it generally has a few hairline scratches or so, you should be okay; however, if you have some very noticeable scratches which appear quite solid and apparent without much extra inspection needed into examining for more detailed scratches, then you're better off trying to exchange it for another copy or getting your money back because I believe it's the disc's fault for having such errors. The game is know to have certain pauses during gameplay randomly where the PS2 will have trouble reading the game although this should happen on very rare occasions. Though I must add, the difference can be in the system sometimes. For example, my original Dragon Quest 8 game has a few pretty bad scratches which appear slightly white (not good of course) and when I tried to pop it up on my old fat v5/v6 PS2, it couldn't play at all; however, when I used my v15 silver slim PS2 it reads perfectly without any hitches at all.
I could claim my old fat PS2's laser is finally kicking the bucket and near its end, but I beg to differ because I can still easily play God of War, Valkyrie Profile: Silermia and Kingdom Heart games fine. As for a solution, it would be best to test your originals. Comparing how your system reads backed-up games with your originals is almost like comparing the blue-colored PS2 CD games with your PSX games. It's quite hard to say the least to get a blue-colored game like Growlanser Generations to play compared to my old PSX Chrono Cross game; and, by the way, both conditions on both discs were mint at least so it couldn't be that.
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