Is this happening to original CDs?
CDs read from the inside of the circle to the outside in a spiral. If your laser head has acquired a limit problem from mechanical issues, it will simply stop at a certain part. Check it with an original disc to make sure it isn't just mechanical.
Also, if it is an older one, which yours seems to be, maybe it can't handle the CDs that put more data on. Like a 650 compared to a 700. The 700, like a DVD, can use a more compacted laser beam path. Once it gets to a certain part of the CD, it just loses the bumps of data because it's too compact for it to understand. At least that's what I've been taught.
You do know that the info isn't closer to the clear side of the CD, but on the label side, right? If you mess with the label side, scratch it, whatever, it won't read again. The layer of gray for recording is right under it. The clear side, bottom, is thicker to protect it from the tray. You can make light scratches on that side, buff it clear again and keep using it. Make sure your label side isn't tampered with the whole way to the edges.
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