Disc Read Error means that the ps2 laser isn't powerful enough to read the data from the disc. The disc may very well have a valid image on it but due to different reflective properties of various types/formats of disc the ps2 laser head just ain't up to the job of readin them.
Not a valid ps2 disc means that the ps2 has read the disc and decided that its not playable, i.e DVDVideo,PS2 or PS1 format.
Advice is stop using rewritables (of either format)as yr ps2 laser isn't up to the job of reading them. As for why yr ps2 reads +r but not -r is strange. It is usually the other way round. Try using some more PS2 friendly DVD-R media like Ritek G4 dvd-r. If still not working then stick with what works (+r dvd's). There is no mod that sony carries out that would make yr ps2 read +r but not -r.
Hope this helps
